# In view of the fact that IN CLASS LOGIC EXERCISES

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1 IN CLASS LOGIC EXERCISES Instructions: Determine whether the following are propositions. If some are not propositions, see if they can be rewritten as propositions. (1) I have a very refined sense of smell. (2) Not here, Bob! (3) I think I m going to sell little Joey into slavery. Instructions: Identify the premises and conclusions in the following arguments, and identify any premise and conclusion indicators. (4) English is the best language since it s the only one that I speak. (5) Bob likes to argue all the time, and for that reason he would make a good lawyer. (6) In view of the fact that Joe cheated on his taxes, we consequently cannot appoint him to the ethics committee. Instructions: Diagram the following arguments. First number each statement, then use plus signs and arrows to designate the argument structure as either a joint inference or an independent inference. (7) Joe has no friends since the only people he knows are on Facebook, and those aren t real friends. (8) Bob was voted most popular student in class, and Bob is always seen with lots of people around him. Thus, Bob has many friends. (9) Joe and Bob aren t friends because each says that he can t stand the other, and each angrily insults the other when they pass in the hall. Premise Indicators Since For Because Given that For the reason that In view of the fact that Conclusion Indicators Therefore Thus Hence So Accordingly For this reason Consequently It follows that Argument Diagrams Joint inference: Independent inference: 1 3 and 2 3

3 Instructions: In each of the following identify the logical connective being used and translate the proposition into standard form. (15) Father Joe s marriage to Beth implies that he first leaves the priesthood. (16) I was accepted at Yale University, but I d much rather attend Thrift Community College. (17) Bob s name does not appear on Santa s nice list. Instructions: Determine which of the following are well-formed nested propositions. (18) if P then (Q or R) (19) (P and Q) not (20) not (P or Q) (21) P and (if Q then R) Conditional: if P then Q Negation: not P Conjunction Clue Words ( And ) P, but Q P, although Q P; Q P, besides Q P, however Q P, whereas Q Conditional Clue Words ( If- Then ) If P, it follows that Q P implies Q P entails Q Whenever P, Q P, therefore Q Q follows from P Q, since P Logical Connectives Conjunction: P and Q Disjunction: P or Q

4 Instructions: Translate the following premises and conclusions into standard form and decide which valid argument form or fallacious argument form is being used. (22) If the band Satan s Pitchfork performs in town, they will play Hell, Sweet Hell. If they perform Hell, Sweet Hell then dudes will stage dive. Therefore, if they perform, dudes will stage dive. (23) Either Bob will go bankrupt, or I will. Bob will go bankrupt. Therefore, I will not. (24) If Joe flunks out of college, then his brother Bob will inherit the family business. Joe will not flunk out of college. Therefore, Bob will not inherit the family business. Instructions: Make up a valid argument that leads to the conclusion given. Use the rule indicated in parentheses. You will need to invent some simple proposition to make your premises complete. (25) Polly wants a cracker. (disjunctive syllogism) (26) If you insult Beth s mother, you will go to the hospital. (hypothetical syllogism) (27) Joe will fail his exam. (modus ponens) (28) Thrift Community College is a good school. (modus tollens) Modus Ponens premise (2) P concl. (3) Therefore, Q Modus Tollens premise (2) Not Q concl. (3) Therefore, not P Disjunctive Syllogism (two versions) premise (1) P or Q premise (2) not P concl. (3) therefore, Q Hypothetical Syllogism premise (1) if P then Q premise (2) if Q then R concl. (3) Therefore, if P then R

5 Instructions: Are the following arguments valid, invalid, sound, or unsound? (29) If Fido is a Dalmatian, then Fido would have lots of spots It is not the case that Fido is a Dalmatian Therefore, it is not the case that Fido has lots of spots (30) If Joseph Stalin had U.S. citizenship, then he would have been born in the U.S. It is not the case that Joseph Stalin was born in the U.S. Therefore, it is not the case that Joseph Stalin had U.S. citizenship. Instructions: The following test your understanding of soundness. (31) Can a valid argument have a false conclusion? (32) Can a sound argument have a false conclusion? Modus Ponens premise (2) P concl. (3) Therefore, Q Modus Tollens premise (2) Not Q concl. (3) Therefore, not P Disjunctive Syllogism (two versions) premise (1) P or Q premise (2) not P concl. (3) therefore, Q Hypothetical Syllogism premise (1) if P then Q premise (2) if Q then R concl. (3) Therefore, if P then R

6 Instructions: What is the inductive strength of each of the following (that is, very strong, strong, weak, very weak)? (33) Some notable guitarist have died in their 20s. Joe is a notable guitarist. Therefore, Joe will probably die in his 20s. (34) College dropouts make \$1 million less during their careers than college graduates. Joe is a college dropout. Therefore, Joe will probably make around \$1 million less during his career than an average college graduate. (35) College students with seven or more body piercings have a significantly higher rate of deviant behavior than students with no piercings. Joe has only one body piercing. Therefore Joe has only a slightly higher rate of deviant behavior than students with no piercings. Inductive Probability Inductively very strong: probability is close to certain. Inductively strong: probability is high. Inductively weak: probability is low. Inductively very weak: probability is close to non-existent.

7 Instructions: For each of the following, indicate the inductive argument form that is followed, and whether it commits any inductive fallacy. (36) Joe and Bob live in the same town, listen to the same music, and like the same sports teams. Joe is Presbyterian. Therefore, Bob is probably also Presbyterian. (37) 60% of college students in the U.S. are women. Preppy State University is a U.S. College. Therefore, there is a very high probability that the next student who walks out of Preppy State s student center will be a woman. (38) 100% of 20 randomly surveyed adults in the small town of Hornbeak, Tennessee shop at Walmart. Therefore, 100% of Americans shop at Walmart. Statistical syllogism: drawing a conclusion about an individual based on the population as a whole. premise (1) n percentage of a population has attribute A. premise (2) x is a member of that population. concl. (3) Therefore, there is an n percent probability that x has A. Fallacy of small proportion: a conclusion is too strong to be supported by the small population proportion with the attribute. Statistical induction: drawing a conclusion about a population based on a sample. premise (1) n percent of a sample has attribute A. concl. (2) Therefore, n percent of a population probably has attribute A. Fallacy of small sample: a conclusion is too strong to be supported by a small sample number. Fallacy of biased sample: a conclusion is too strong to be supported by a nonrandom sampling technique. Argument from Analogy: drawing a conclusion about one individual based on its similarities with another individual. premise (1) Objects x and y each have attributes A, B and C. premise (2) Object x has an additional attribute D. concl. (3) Therefore, object y probably also has attribute D. Fallacy of false analogy: comparing two items that have trivial points in common, but differ from each other in more significant ways.

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