Basic Argument Forms

Question 1

Modus Ponens (MP)

Answer 1

(p → q)
p
∴ q

Question 2

Modus Tollens (MT)

Answer 2

(p → q)
¬q
∴ ¬p

Question 3

Hypothetical Syllogism (HS)

Answer 3

(p → q)
(q → r)
∴ (p → r)

Question 4

Disjunctive Syllogism (DS)

Answer 4

(p ∨ q)
¬p
∴ q

Question 5

Constructive Dilemma (CD)

Answer 5

(p → q)
(r → s)
(p ∨ r)
∴ (q ∨ s)

Question 6

Destructive Dilemma (DD)

Answer 6

(p → q)
(r → s)
(¬q ∨ ¬s)
∴ (¬p ∨ ¬r)

Question 7

Composition

Answer 7

(p → q)
(p → r)
∴ (p → (q ∧ r))

Question 8

De Morgan’s Theorem (1)

Answer 8

¬(p ∧ q)
∴ (¬p ∨ ¬q)

Question 9

De Morgan’s Theorem (2)

Answer 9

¬(p ∨ q)
∴ (¬p ∧ ¬q)

Question 10

Transposition

Answer 10

(p → q)
∴ (¬q → ¬p)

Question 11

Material Implication

Answer 11

(p → q)
∴ (¬p ∨ q)

Question 12

Exportation

Answer 12

((p ∧ q) → r)
∴ (p → (q → r))

Question 13

Importation

Answer 13

From (if q is true then r is true, if p is true) we can prove (if p and q are true then r is true).
(p → (q → r))
∴ ((p ∧ q) → r)

Question 14

Tautology (1)

Answer 14

p
∴ (p ∨ p)

Question 15

Tautology (2)

Answer 15

p
∴ (p ∧ p)

Question 16

Tertium non datur (Law of Excluded Middle)

Answer 16

∴ (p ∨ ¬p)