The Little Blue Reasoning Book Part 12

Debraas statement above is also equivalent to the following: If a person is a good salesperson, then he or she must be friendly.

Now letas summarize what Tom thought Debra said: If a person is friendly, then he or she will make a good salesperson.

Tom has effectively reversed the original aIfaaathena statement and erroneously committed the fallacy of affirming the consequent. Tom would have been correct had he instead responded, aOh, what you mean is that only friendly people are capable of making good salespersons,a or aI agree, a good salesperson must be friendly,a or aThatas right. If youare not friendly, then youare not going to make a good salesperson.a Choice B is a correct transcription of Debraas original statement comment. It cannot be correct because Tom disagrees with her. Choice E is a logical inference based on Debraas original statement (it is the contrapositive!). Choices A and D are not correct because regardless of whether the statements are true in themselves they do not lie at the crux of Tomas misunderstanding.

Back to problem Problem 37: Football Choice A. According to the rules of logical equivalency, the statement, aEvery person on the Brazilian World Cup football team is a great player,a may be translated as, aIf a person is on the Brazilian World Cup football team, then he is a great player.a And this may be further translated as, aOnly great players are Brazilian World Cup football players.a Choice A cannot be true. The statement, aOnly Brazilian World Cup football players are great playersa is exactly what Beth has misunderstood Marieas remark to mean. Beth thinks Marie has said, aBrazil has all the great World Cup football players.a Choices B, C, D, and E are all unwarranted inferences.

Back to problem Problem 38: Medical Hierarchy Choice A. With reference to the diagram below, the dotted circle representing researchers crosses into the solid inner circle representing surgeons, so we know for certain that at least some surgeons are researchers. Note that the solid circle representing surgeons is inside the larger solid circle representing doctors, which is inside the still larger solid circle representing medically licensed individuals.

For answer choices B through E, check for why each of these acould be truea and, in this way, eliminate them from contention as possible correct answers. choice B could be true, as indicated by the area within the circle representing surgeons that appears above the dotted line (see embedded letter aBa). Choice C could be true, as indicated by the area outside the circle representing surgeons but within the circle representing doctors and within the dotted line (see embedded letter aCa). Choice D states basically the same thing as choice B. Some doctors/surgeons are researchers, but not all doctors/surgeons are researchers. Choice E could be true if the dotted circle extends beyond the solid circle representing medically licensed individuals (see embedded letter aEa).

Problem 39: Valley High School Choice E. With reference to the following diagram, if all physics students study math and no math students study French, then it must be true that no physics students study French. In referring to the diagram below, the little black circle (i.e., physics) must stay inside the larger black circle representing math students.

Again, the best way to eliminate wrong answer choices is to see which ones acould be true.a Choice A is incorrect because the smaller dotted circle could be anywhere as long as it partially overlaps with the larger dotted circle representing English students. Choice B is incorrect because the little black circle representing physics students may or may not be within the larger dotted circle representing English students. Choice C is very tricky indeed because the small solid circle could be expanded to fit perfectly in the larger math circle. In this case, all physics students could be math students and all math students could be physics students, however unlikely. Choice D is also tricky. Should the large dotted circle representing English students be quite large, then it would be true that most math students study English but that most English students are not also studying math.

Back to problem Problem 40: Little Italy 1. Not inferable. We cannot infer that Antonioas restaurant is the best in the city. We could, however, infer that his restaurant is among the best Italian restaurants in the city.

2. Not inferable. We can infer that Antonio is good at preparing Italian food, but we cannot infer logically that he alikesa preparing Italian food. He may in fact find preparing food very tedious and boring.

3. Not inferable. There is nothing to say that three out of every four Food and Beverage consultants do not also recommend a number of other Italian restaurants in the city. Which restaurant they recommend most is unclear.

4. Not inferable. This is a tad technical. aAntonioas customers prefer his style of Italian cooking by a ratio of 2 to 1.a This original statement does not contain a logical comparative. In other words, it could be comparing Antonioas Italian cooking to mice, dog food, or to the common cold.

The following is a statement from which a proper inference could be drawn: aAntonioas customers prefer his style of Italian cooking to that of other comparable Italian restaurants by a ratio of 2 to 1.a 5. Not inferable. We simply do not know.

6. Not inferable. Tricky a" even if Antonio is a connoisseur of Italian food, capable of preparing high-quality dishes, we do not know that he actually prepares high-quality food or whether he uses the highest-quality ingredients. For all we know, customers love Antonioas restaurant because of its location and ambience, not because the food is necessarily great. Note that the qualitative terms such as awell-known,a afamous,a or asuccessfula may not translate to their often-a.s.sumed monetary equivalents of aricha or aprofitable.a 7. Not inferable. For all we know, Little Italy is a very popular restaurant even though it is inefficiently run and barely breaks even.

8. Not inferable. We cannot tell what would happen in another city or, for that matter, even in another location within Devon city.

9. Not inferable. We do not know. Customers may crowd the restaurant paying top dollar or they may fill the restaurant paying moderate prices.

10. Not inferable. Again, this is subtle. We may infer that Antonio spent a number of years preparing to become an Italian connoisseur, but he may have attained his reputation as an Italian connoisseur in a relatively short period of time.

Back to problem APPENDIX III a" a.n.a.lOGIES Problem 41: a.n.a.logy Exercise Back to problem 1. RED is to PINK as BLACK is to GRAY. The relations.h.i.+p is one of intensity or degree. Pink is a muted form of red; gray is a muted form of black. White is the opposite of black, while dark is a characteristic of black.

C. Type of a.n.a.logy: Degree 2. HEAT is to RADIATOR as BREEZE is to FAN. The relations.h.i.+p is that of the effect to its cause. Both wind and a fan can cause a breeze, so you must further refine the relations.h.i.+p. Artificial heat is produced by a radiator; an artificial breeze is produced by a fan.

D. Type of a.n.a.logy: Cause and Effect 3. BIG is to LARGE as WIDE is to BROAD. High and long are dimensions, but they are not synonyms for WIDE. Small is an imperfect antonym. Broad means wide.

B. Type of a.n.a.logy: Synonym 4. DOG is to CAT as CROCODILE is to LIZARD. Both a dog and a cat are part of a larger cla.s.sification called amammals.a Both a crocodile and a lizard are part of a larger cla.s.sification called areptiles.a Both the hippopotamus and the elephant are mammals.

C. Type of a.n.a.logy: Part to Part 5. FLOWER is to BOUQUET as LINK is to CHAIN. A flower forms part of a bouquet as a link forms part of a chain.

D. Type of a.n.a.logy: Part to Whole 6. TOMORROW is to YESTERDAY as FUTURE is to PAST. This is a sequential relations.h.i.+p. By definition, the relations.h.i.+p of yesterday, today, and tomorrow is a.n.a.logous to the past, present, and the future. Present occupies the wrong place in the sequence; it is a.n.a.logous to today rather than yesterday. aAgoa is correct in its meaning but grammatically wrong.

B. Type of a.n.a.logy: Sequence 7. HERO is to VALOR as HERETIC is to DISSENT. The characteristic which makes one a hero is valor (courage); the characteristic which makes one a heretic is dissent from religious doctrine.

A. Type of a.n.a.logy: Characteristic 8. PRESENT is to BIRTHDAY as REWARD is to ACCOMPLISHMENT. A birthday is a.s.sociated with receiving presents. An accomplishment is a.s.sociated with receiving a reward. Medal and money are both types of rewards, not reasons for it.

A. Type of a.n.a.logy: a.s.sociation 9. SKY is to GROUND as CEILING is to FLOOR. The roof is above the ceiling but is not opposite to it. Top and plaster are descriptive of ceiling.

A. Type of a.n.a.logy: Antonym 10. MONEY is to BANK as KNOWLEDGE is to BOOKS. One function of a bank is to hold money; one function of books is to hold knowledge.

D. Type of a.n.a.logy: Function or Purpose APPPENDIX IV a" THE 10 CLa.s.sIC TRADE-OFFS Problem 42: Matching Exercise Back to problem 1. Fossil Fuels F. Short-term vs. Long-term trade-off Sometimes the only difference that stands between two opposing points of view is differing time frames. In other words, two people might well agree on a given solution but simply disagree as to when the solution might come about.

One of the most basic ways to view a problem is in terms of short-term vs. long-term time frames. In this example, two people argue that solar energy is the solution to our current energy needs: one person effectively says aI agreea and another says aI disagree.a However, it is not that both persons disagree on solar energyas being a great alternative, but rather, they disagree on when it will become a viable alternative. In a short-term vs. long-term trade-off, two people agree on a given course of action but believe that it will be implemented during different time frames.

2. Miracle Tablets E. Quant.i.ty vs. Quality trade-off The issue here centers on how much pain reliever you get for your money. Quality equals the amount of pain reliever per tablet; quant.i.ty equals the price of a pain reliever, taking into consideration the number of tablets.

This problem is built on the a.s.sumption that you get twice the amount (quant.i.ty) of pain reliever for the same price, since Miracle tablets contain twice as much pain reliever with an identical price per bottle. Of course, the amount of pain reliever is a function of both the quality of pain reliever in each tablet as well as the number of tablets per bottle. The a.s.sumption, therefore, is that both competing bottles will contain the same number of tablets. If a bottle of regular aspirin contains twice as many tablets as a bottle of Miracle, the advantage effectively disappears.

What is likely to be the case here is that both bottles of pain reliever are the same size. Miracle tablets are twice as large as regular aspirin tablets, but a bottle of Miracle contains half as many tablets as a bottle of regular aspirin. Predictably a Miracle tablet contains twice as much pain reliever per tablet compared with regular aspirin. Thus, itas all a wash. Weare getting the exact same amount of pain reliever per bottle. Consumeras choice a" would one prefer to take one big tablet or two small tablets to get the same amount of pain reliever?

3. Pirates B. Breadth vs. Depth trade-off According to this problem, music fans would be better served by a wider, costlier selection of music CDs than by a narrower, cheaper selection. This argument is grounded on the a.s.sumption that greater variety (abreadtha) is better than less variety (adeptha).

4. Techies G. Specific vs. General trade-off According to this argument, the reason people achieve top-level management jobs is that they develop a.n.a.lytically rigorous mindsets which come from their broader liberal arts-based education. All we have to do to weaken this argument is to suggest that vocationally trained individuals also develop a.n.a.lytically rigorous mindsets. For example, intensive training in a limited field such as computer programming may develop a.n.a.lytical skills as much as a broader liberal arts education does.

5. Workers I. Theory vs. Practice trade-off Working in an industry gives one practical experience. Studying an industry gives one a conceptual understanding of how that industry works. Working in an industry, however, does not guarantee that one understands the nuances of how that industry operates, especially at the macro level. Likewise, studying an industry does guarantee that one can grasp the nuances of how workers actually get things done in that industry. In this scenario, it is unclear whether those who work as union executivesaa"acollege trained lawyers, economists, and labor relations officersaa"aare incapable of grasping the inner workings of their industry (unionized labor). It is also unclear whether those who might come up through the ranks of the labor unions to become executives would be in a better position to manage and deal with the macro issues in which that industry operates.

6. Sales D. Means vs. Ends trade-off This problem pivots primarily on a ameans vs. endsa trade-off and, in particular, on differing means. That is, the prospect of hiring more salespeople or conducting a market survey is based on differing means, while the decision to increase sales is based on an identical goal (end result).

7. Safe Haven A. Control vs. Chance trade-off The issue pivots on the difference between random violence and the violence that can be avoided by taking reasonable precautions. The conclusion that parents should not consider moving to the suburbs is weakened by the idea that parents exercise some control over their childrenas behavior in the suburb scenario. A parent has a lot less of a chance to prevent teenage death due to a drive-by shooting than a death due to suicide or driving while intoxicated. This highlights a control vs. chance trade-off.

8. Free Speech C. Individual vs. Collective trade-off The argument basically says that free speech should know no limits. However, when free speech is deemed injurious to the collective rights of the agroup,a it is not allowed. In this respect, individual and collective rights trade-off with one another. We have free speech but in certain situations the rights of the group take precedence.

9. Historians H. Subjective vs. Objective trade-off Per the topic at hand, the historianas success in being scientifically objective is at best illusory because, here, objectivity is linked to detachment and is deemed incompatible with pa.s.sion. Thus we have a subjective vs. objective trade-off.

10. My Land J. Tradition vs. Change trade-off This problem gives rise to a rather interesting example, tying the tradition vs. change trade-off to argument by a.n.a.logy.

In this tradition vs. change trade-off, Nordwell was saying, aOkay let tradition prevail: Iall take Italy because Columbus took America.a Likewise, according to argument by a.n.a.logy, Nordwell was saying, aBecause Columbus could claim America, I can claim Italy. But of course, I have no right to claim Italy, as Columbus had no right to claim America.a APPENDIX V a" CRITICAL READING AND COMPREHENSION For an in-depth review of the strategies used to answer reading comprehension questions, including coverage of The Four-Corner Question Cracker for Reading Comprehensiona", refer to Appendix VI a" Tips for Taking Reading Tests.

Problem 43: Sample Pa.s.sage Back to problem Question 1 Choice D. This is an overview question. Look for the words of the topic and avoid overly detailed or overly general answer choices.

Choice A is too general because a discussion of educational philosophy in the last forty years would likely incorporate the viewpoints of many individuals, not just the authoras viewpoint. Choice B is outside the pa.s.sageas scope. We do not necessarily know whether or not teachers should receive more liberal arts training. Choice C is a correct statement within the pa.s.sageas context. However, it is too detailed to satisfy the primary purpose as demanded by this overview question.

For an overview question, there are effectively five reasons why wrong answers could be wrong. An answer choice will either be outside a pa.s.sageas scope, opposite in meaning, distorted in meaning, too general, or too detailed. Whereas choice C was too detailed, choice A is an overly general answer choice. It is very useful to be on the lookout for aout of the scopea-type answers. This was the fate of answer choices B and E. Note that opposites or distortions are not common wrong answer choices with regard to overview questions.

A time-honored tip for answering overview questions involves performing a atopic-scope-purposea drill. That is, we seek to identify the pa.s.sageas topic, scope, and purpose. Topic is defined as the pa.s.sageas broad subject matter. Itas an aarticle on education.a The topic is therefore aeducation.a Scope is defined as the specific aspect of the topic that the author is interested in. The scope here is aschooling versus education.a Last, purpose is defined as the reason the author sat down to write the article. His purpose is to say: aColleges or universities canat educate; they exist to prepare students for later learning because youth itself makes real education impossible.a Knowing the topic, scope, and purpose is enough to answer directly the question at hand. And knowing the authoras purpose will likely set us up for another right answer on at least one of the remaining questions. Identifying the topic alone can help get us halfway to a right answer because the correct answer to an overview question almost always contains the words of the topic. In this case, the word aeducationa (or its derivative aeducateda) does not appear in answer choices B or E. We can feel fairly confident eliminating both of these choices.

Question 2 Choice E. This is an explicit-detail question which enables the reader to go back into the pa.s.sage and effectively underline the correct answer. Look for a very literal answer.

Where is the correct answer to be found? Consider the words aprepare the young for continued learning in later life by giving them the skills of learninga (1st paragraph) and abetter off if their schooling had given them the intellectual discipline and skilla (3rd paragraph). The word askilla surfaces both times that the author talks about what schools should be doing.

Choice A is outside the pa.s.sageas scope. The pa.s.sage does not talk about improving academic instruction or have anything to do with gra.s.sroots education levels. Nor does the pa.s.sage talk about adultsa opinions. Choice B is essentially opposite in meaning. To be correct, the answer choice should read, aredefine aeducationa as aschoolinga so to better convey to parents the goals of teaching.a The author feels that adults have missed the point in thinking that finis.h.i.+ng school is the same as finis.h.i.+ng oneas education; in fact, schools exist to school, and education comes later. Choice D may be also cla.s.sified as opposite in meaning, if we stick to the general spirit of the pa.s.sage. The author believes that adults are very much uninformed and have missed the major point of education (3rd paragraph); therefore closely implementing their opinions is essentially opposite to the authoras intended meaning.

Choice C is a distorted meaning. Distortions are most often created by the use of extreme or categorical or absolute-type wordings. Here the word aonlya signals a potential distortion. The author would likely agree that high scholastic achievement is a possible requirement for becoming educated, but not a sufficient condition in and of itself. In fact, the author really doesnat mention scholastic achievement, so we might cla.s.sify it as being out of scope if we did not happen to focus initially on the absolute-type wording.

Question 3 Choice B. This is an inference question. The challenge is to find an answer that isnat explicitly mentioned in the pa.s.sage, but can be logically inferred.

Although the author does not give an exact aeducationa formula, he effectively says that a number of factors are necessary to travel the high road to becoming educated. These include: pa.s.sion, a knack for learning, discipline, and maturity. In terms of maturity, he clearly states, aThe young can be prepared for education in the years to come, but only mature men and women can become educated, beginning the process in their forties and fifties and reaching some modic.u.m of genuine insight, sound judgment and practical wisdom after they have turned sixty.a Obviously, according to the author, if maturity begins in a personas forties and takes another ten to twenty years, then an individual cannot be less than forty years of age and still be considered educated.

Wrong answer choices in inference-type questions often fall outside the pa.s.sageas scope. Choice A is outside the pa.s.sageas scope and is specifically referred to as an unwarranted comparison. The author does not say whether he believes becoming educated takes more pa.s.sion than maturity or more maturity than pa.s.sion.

Choice C is perhaps the trickiest wrong answer choice. The author doesnat imply that one has to be a university graduate. In fact, he mentions aschool and/or collegea (1st & 3rd paragraphs), which suggests that he may well lump high school in with college and/or university. A high school graduate might have enough schooling to get onto the road of education. Moreover, the author doesnat claim one must be a four-year college or university graduate or even whether one has to attend college or university.

There is no mention of cla.s.sic works of literature, so choice D is outside the pa.s.sageas scope; we cannot answer this question based on information presented in the pa.s.sage. Choice E is wrong because the author never mentions atravel.a Donat mistake the word atravaila (meaning astrugglea; 4th paragraph) for atravel.a Moreover, it is possible, without evidence to the contrary, that a person could never have left his or her own country and still understand those ideas that make him or her representative of his or her particular culture.

Question 4 Choice A. This is a tone question. Tone questions ask about the authoras feeling or att.i.tude toward someone or something in the pa.s.sage. Basically, the author will be either positive, negative, or neutral. In most cases, especially with respect to social science pa.s.sages (versus science pa.s.sages), the fact that the author would sit down to write something hints that he or she has some opinion about the topic at hand. Therefore, the neutral answer choice is not usually correct, even if available.

For this question, we have, on the positive and supportive side, the word pairs ainvaluable partners,a aconscientious citizens,a or aunfortunate victims.a On the negative side, we have auninformed partic.i.p.antsa or adisdainful culprits.a The authoras att.i.tude toward adults is somewhat negative, but not excessively so. The feeling is more like frustration. The author believes that adults are ignorant of the distinction between schooling and education (3rd paragraph). Therefore, positive-sounding choices C and D are out. Choice B, aunfortunate victims,a is sympathetic, but the author thinks that adults are not victims, just misfocused. Choice E, adisdainful culprits,a is too negative.

Question 5 Choice C. This is a pa.s.sage organization question. Think in terms of the number of viewpoints and the relations.h.i.+ps among them.

The author introduces his thesis or summary in the very first sentence a" aa controlling insight in my educational philosophya a" then goes on to support it with his personal observations, experiences, and opinions. Thus, choice A is not correct. No objective a.n.a.lysis is put forth; if there were, we would expect to see some surveys, statistics, or alternative viewpoints introduced. Choice B is wrong because there is a single idea presented, but the author agrees with it because it is his own idea. Choice D is incorrect as there are not two viewpoints presented, just one. Choice E suggests a popular viewpoint, but it is highly unlikely that many people have adopted this viewpoint because, according to the author, adults (and, by extension, laypersons) havenat really caught on. Last, a number of perspectives are not drawn upon. The author chooses to spend the entire article developing his single viewpoint that ano one has ever been a" no one could ever be a" educated in school or college.a Quiz a" Answers

Back to quiz questions

1. False. The Prisoneras Dilemma provides an example of how cooperation is superior to compet.i.tion.

(Tip #17, Chapter 3 a" Decision Making) 2. False. The statement asome doctors are rich peoplea does imply reciprocality because asome rich people must be doctors.a (Tip #49, Chapter 5 a" Mastering Logic) 3. False. The ad hominem fallacy consists in attacking the person, often in a personal or abusive way, rather than attacking the argument or claim being made. Attempting to draw attention away from the real issue by emphasizing a side issue describes the fallacy known as ared herring.a (Ad Hominem vs. Red Herring, Appendix II a" Fallacious Reasoning) 4. False. The halo effect is the tendency to view a person, place, or thing favorably based on only a single incident, trait, or characteristic.

(The Magic of Coincidence, Chapter 1 a" Mindset & Perception) 5. False. The formulaic relations.h.i.+p among the three elements of cla.s.sic argument structure is: Conclusion = Evidence + a.s.sumption or Conclusion a' Evidence = a.s.sumption (Problem 38, Chapter 4 a" a.n.a.lyzing Arguments) 6. False. The words ainferencea and aa.s.sumptiona are not the same and should not be used interchangeably. An ainferencea is a logical deduction based on an argument, statement, or written pa.s.sage. An a.s.sumption is an integral component of an argument.

(Avoiding Improper Inferences, Chapter 5 a" Mastering Logic) 7. False. Matrixes can be used to summarize data within a two-dimensional grid. Data must be amutually exclusive and collectively exhaustive,a not acollectively exclusive and mutually exhaustive.a (Tip #4, Chapter 2 a" Creative Thinking) 8. False. In formal logic, the phrase aEvery A is a Ba must be translated as aOnly Bs are As,a not aOnly As are Bs.a Case in point: The statement aEvery cat is a mammala must be translated as aOnly mammals are cats.a It is not true to say that if every cat is a mammal then only cats are mammals.

(Tip #47, Chapter 5 a" Mastering Logic) 9. False. Left-brain thinking might be described as aspotlighta thinking, while right-brain thinking might be described as afloodlighta thinking.

(Divergent vs. Convergent Thinking; Chapter 2 a" Creative Thinking) 10. False. Utility a.n.a.lysis takes into account the desirability of outcomes by multiplying each value by the probability of its occurrence. We do not total resultant values; we choose the outcome which yields the highest value.

(Utility a.n.a.lysis vs. Weighted Ranking, Chapter 3 a" Decision Making) Selected Bibliography Adams, James L. Conceptual Blockbusting: A Guide to Better Ideas, 4th ed. Cambridge, MA: Perseus Publis.h.i.+ng, 2001.

Adler, Mortimer and Geraldine Van Doren. Reforming Education: The Opening of the American Mind. New York: Macmillan, 1988.

Bennett, Deborah J. Logic Made Easy: How to Know When Logic Deceives You. New York: W.W. Norton, 2005.

Bransford, John D. & Barrry S. Stein. The Ideal Problem Solver: A Guide for Improving Thinking, Learning, and Creativity. 2nd ed. New York: Worth, 1993.

Buzan, Tony. Use Both Sides of Your Brain: New Mind-Mapping Techniques, 3rd ed. New York: Plume, 1991.

Cause, Donald C. & Gerald M. Weinberg. Are Your Lights On? How to Figure Out What the Problem Really Is. New York: Dorset House, 1990.

Copi, Irving M. & Carl Cohen. Introduction to Logic. 13th ed. Englewood Cliffs, NJ: Prentice Hall, 2008.

Damer, T. Edward. Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments. Belmont, CA: Wadsworth, 2008.

de Bono, Edward. The Use of Lateral Thinking. New York: Penguin, 1986.

Harrison, Allen F. & Robert M. Bramson. The Art of Thinking. New York: Berkeley Books, 2002.

How to Prepare for the Graduate Record Examination: GRE General Test. 17th ed. Hauppauge, NY: Barronas Educational Series, 2007.

Jones, Morgan D. The Thinkeras Toolkit: 14 Powerful Techniques for Problem Solving. New York: Times Books, 1998.

The Official Guide for GMAT Verbal Review. 2nd ed. Hoboken, NJ: Wiley, 2009.

Russo, J. Edward & Paul J.H. Schoemaker. Decision Traps: The Ten Barriers to Brilliant Decision-Making and How to Overcome Them. New York: Fireside, 1990.

Salny, Dr. Abbie F. & Lewis Burke Frumkes. Mensa Think-Smart Book: Games and Puzzles to Develop a Sharper, Quicker Mind. New York: Harper and Row, 1986.

Sternberg, Robert J. Intelligence Applied: Understanding and Increasing Your Intellectual Skills. Orlando, FL: Harcourt Brace Jovanovich, 1986.

Steinberg, Eve P. Scoring High on a.n.a.logy Tests. New York: Arco, 1990.

Stewart, Mark A. GRE-LSAT Logic Workbook. 3rd ed. New York: Arco, 1999.

Thomson, Anne. Critical Reasoning: A Practical Introduction. New York: Routledge, 2008.

Thouless, Robert H. Straight and Crooked Thinking. London: Hodder, 1990.

Weston, Anthony. A Rulebook for Arguments. 4th ed. Indianapolis, IN: Hackett, 2008.

Whimbey, Anthony & Jack Lockheed. Problem Solving & Comprehension. 6th ed. Hillsdale, NJ: Lawrence Erlbaum, 1999.

Wikipedia, The Free Encyclopedia, s.v. aFallacy,a http://en.wikipedia.org/wiki/Fallacy * * *

I have never let my schooling

interfere with my education.

a"Mark Twain