Logical Forms

Question 1

Modus Ponens

Answer 1

Deductively valid form where Q is inferred from the premises “If P then Q” and “P”

If P then Q
P
—————
Q

Question 2

Modus Tollens

Answer 2

A deductively valid form in which “not P” is inferred from “If P then Q” and “not Q”

If P then Q
Not Q
—————-
Not P

Question 3

Affirming the Consequent

Answer 3

Deductively invalid logical form where P is inferred from the premises “if P then Q” and “Q”

If P then Q
Q
—————
P

Opposite from modus ponens

Question 4

Denying the Antecedent

Answer 4

Deductively invalid logical form where not-Q is inferred from the premises “If P then” and “not P”

If P then Q
Not P
—————-
Not Q

Opposite of modus tollens

Question 5

Disjunctive Syllogism

Answer 5

Deductively valid form that uses disjunction

Either P or Q
Not P
——————-
Q

Question 6

Hypothetical Syllogism

Answer 6

A deductively valid form in which “If P then R” is inferred from “If P then Q” and “If Q then R”

If P then Q
If Q then R
—————-
If P then R