Standard form argument patterns

Question 1

Argument by Elimination

Answer 1

1.) Either P or Q.
2.) ~ P.
3.) therefore, Q.
________________________
1.) Either P or Q.
2.) ~Q.
3.) therefore, P.

Question 2

Conjunction Argument

Answer 2

1. ) P
2. ) Q
3. ) therefore, P & Q.

Question 3

Simplification Argument

Answer 3

1.) P & Q.
2.) therefore, P.
_________________________
1.) P & Q.
2.) therefore, Q.

Question 4

Affirming the Antecedent (Modus Ponens)

Answer 4

1. ) If P then Q.
2. ) P.
3. ) therefore, Q .

Question 5

Denying the Consequent (Modus Tollens)

Answer 5

1. ) If P then Q.
2. ) ~Q.
3. ) therefore, ~P.

Question 6

Hypothetical syllogism

Answer 6

1. ) If P then Q.
2. ) If Q then R.
3. ) therefore, If P then R.

Question 7

Contraposition

Answer 7

1. ) If P then Q.

2. ) therefore, If ~Q then ~P.

Question 8

Equivalence

Answer 8

1. ) P if and only if Q.
2. ) ~P.
3. ) therefore, ~Q.

Question 9

Universal Modus Ponens

Answer 9

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

Question 10

Universal Modus Tollens

Answer 10

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

Question 11

Universal hypothetical syllogism

Answer 11

1. ) All As are Bs.
2. ) All Bs are Cs.
3. ) therefore, All As are Cs.

Question 12

Universal Ruling Out

Answer 12

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