Identifying Argument Patterns

Question 1

1. PorQ.
2. -P.
3. Q.

Answer 1

Argument by Elimination

Valid Sentential

Question 2

1. IfPthenQ. 2. P.

3. Q.

Answer 2

Affirming the Antecedent

Valid Sentential

Question 3

1. If P then Q.
2. If Q then R.
3. If P then R.

Answer 3

Hypothetical Syllogism

Valid Sentential

Question 4

1. P.
2. Q.
3. P and Q.

Answer 4

Conjunction

Valid Sentential

Question 5

1. If P then Q.
2. -Q.
3. -P.

Answer 5

Denying the Consequent

Valid Sentential

Question 6

1. If P then Q.

2. If -Q then -P.

Answer 6

Contraposition

Valid Sentential

Question 7

1. P and Q

2. P.

Answer 7

Simplification

Valid Sentential

Question 8

1. • -P

2. P

Answer 8

Double Negation

Valid Sentential

Question 9

1. P ifandonlyif Q.
2. -P.
3. -Q.

Answer 9

Equivalence

Valid Sentential

Question 10

1. If P then Q.
2. -P
3. -Q.

Answer 10

Denying the Antecedent

Invalid Sentential

Question 11

1. If P then Q.
2. Q.
3. P.

Answer 11

Affirming the Consequent

Invalid Sentential

Question 12

1. All As are Bs.
2. x is an A.
3. x is a B.

Answer 12

Valid Predicate

Question 13

1. All As are Bs.
2. All Bs are Cs.
3. All As are Cs.

Answer 13

Valid Predicate

Question 14

1. All As are Bs.
2. x is not a B.
3. x is not an A.

Answer 14

Valid Predicate

Question 15

1. No As are Bs.
2. x is an A.
3. x is not a B.

Answer 15

Valid Predicate

Question 16

1. All As are Bs.
2. x is not an A.
3. x is not a B.

Answer 16

Invalid Predicate

Question 17

1. All As are Bs.
2. xisaB.
3. xisanA.

Answer 17

Invalid Predicate

Question 18

1. Most As are Bs.
2. x is an A.
3. x is a B.

Answer 18

Cogent

Question 19

1. x is an A
2. x is a B
3. Most ABs are Cs.
4. x is a C

Answer 19

Cogent

Question 20

1. Most As are Bs.
2. x is not an A.
3. x is not a B.

Answer 20

Ill Formed

Question 21

1. Most As are Bs.
2. x is a B.
3. x is an A.

Answer 21

Ill Formed

Question 22

Affirming the Antecedent Ex.

Answer 22

1. If the Prime Minister is at 24 Sussex Drive, then the Prime Minister is in Ottawa.
2. The Prime Minister is at 24 Sussex Drive.
3. The Prime Minister is in Ottawa.
   Affirming the Antecedent
4. If P then Q. 2. P.
5. Q.

Question 23

Denying the Consequent Ex

Answer 23

1. If the Prime Minister is at 24 Sussex Drive, then the Prime Minister is in Ottawa.
2. The Prime Minister is not in Ottawa.
3. Prime Minister is not at 24 Sussex Drive.
   Denying the Consequent
4. If P then Q.
5. -Q.
6. -P.

Question 24

Hypothetical Syllogism Ex

Answer 24

1. If the Prime Minister is at 24 Sussex Drive, then the Prime Minister is in Ottawa
2. If the Prime Minister is in Ottawa, then the Prime Minister is not on vacation.
3. If the Prime Minister is at 24 Sussex Drive, then the Prime Minister is not on vacation.
   Hypothetical Syllogism
4. If P then Q. 2. If Q then R. 3. If P then R.

Question 25

3 ways to test for validity:

Answer 25

1. Find a counterexample to the argument.
2. Find a counterexample to the argument’s pattern.
3. Check the list of argument patterns.

Question 26

Define Cogency

Answer 26

CD2: An argument is cogent if and only if it is not valid but it follows a pattern such that all arguments following that pattern have a conclusion that is probably true if the premises are true.