Common valid argument forms

Question 1

Modus Ponens

Answer 1

• If P then Q
• P
• Therefore, Q

Question 2

Modus Tollens

Answer 2

• If P then Q
• Not Q
• Therefore, not P

Question 3

Hypothetical Syllogism

Answer 3

• If P then Q
• If Q then R
• Therefore, if P then R

Question 4

Disjunctive Syllogism

Answer 4

• P or Q
• Not P
• Therefore, Q

Question 5

Constructive Dilemma

Answer 5

• If P then Q, and If R then S
• P or R
• Therefore, Q or S

Question 6

Absorption

Answer 6

• If P then Q

- Therefore, if P then P and Q

Question 7

Simplification

Answer 7

• P and Q

- Therefore, P

Question 8

Conjunction

Answer 8

• P
• Q
• Therefore, P and Q

Question 9

Addition

Answer 9

• P

- Therefore, P or Q

Question 10

Disjunctive Elimination

Answer 10

• P or Q
• If P then R
• If Q then R
• Therefore, R

Question 11

Fallacy of affirming the consequent (converse error)

Answer 11

• If P then Q
• Q
• Therefore, P

Question 12

Fallacy of denying the antecedent (inverse error)

Answer 12

• If P then Q
• Not P
• Therefore, not Q