Forms and Rules

Question 1

Fallacy of affirming the Consequent

Answer 1

If A, then B
B
So, A

Question 2

Fallacy of denying the Antecedent

Answer 2

If A, then B
Not A
So, Not B

Question 3

Modus Ponens (MP)
Implicational Rule

Answer 3

p→q
p
∴ q

Question 4

Modus Tollens (MT)
Implicational Rule

Answer 4

p→q
̴ q
∴ ̴ p

Question 5

Hypothetical Syllogism (HS)
Implicational Rule

Answer 5

p→q
q→r
∴ p→r

Question 6

Disjunctive Syllogism (DS)
Implicational Rule

Answer 6

p ᵥ q p ᵥ q
̴ q ̴ p
∴ p ∴ q

Question 7

Constructive Dilemma (CD)
Implicational Rule

Answer 7

p ᵥ q
p→r
q→s
∴ r ᵥ s

Question 8

Simplification (Simp)

Implicational Rule

Answer 8

p ⦁ q p ⦁ q

∴ p ∴ q

Question 9

Conjunction (Conj)

Implicational Rule

Answer 9

p
q
∴ p ⦁ q

Question 10

Addition (Add)

Implicational Rule

Answer 10

p

∴ p ᵥ q

Question 11

Double Negation (DN)
Equivalence Rule

Answer 11

p ꞉꞉ ̴ ̴ p

Question 12

Commutation (Com)

Equivalence Rule

Answer 12

(p ᵥ q) ꞉꞉ (q ᵥ p)

p ⦁ q) ꞉꞉ (q ⦁ p

Question 13

Association (As)

Equivalence Rule

Answer 13

(p ᵥ (q ᵥ r)) ꞉꞉ ((p ᵥ q) ᵥ r)

p ⦁ (q ⦁ r)) ꞉꞉ ((p ⦁ q) ⦁ r

Question 14

De Morgans Laws (DeM)

Equivalence Rule

Answer 14

̴ (p ⦁ q) ꞉꞉ ( ̴ p ᵥ ̴ q)

̴ (p ᵥ q) ꞉꞉ ( ̴ p ⦁ ̴ q)

Question 15

Contraposition (Cont)

Equivalence Rule

Answer 15

(p → q) ꞉꞉ ( ̴ q → ̴ p)

Question 16

Distribution (Dist)

Equivalence Rule

Answer 16

(p ⦁ (q ᵥ r)) ꞉꞉ ((p ⦁ q) ᵥ (p ⦁ r))

p ᵥ (q ⦁ r)) ꞉꞉ ((p ᵥ q) ⦁ (p ᵥ r)

Question 17

Exportation (Ex)

Equivalence Rule

Answer 17

((p ⦁ q) → r) ꞉꞉ ((p → (q → r))

Question 18

Redundancy (Re)

Equivalence Rule

Answer 18

p ꞉꞉ (p ⦁ p)

p ꞉꞉ (p ᵥ p)

Question 19

Material Equivalence (Me)
Equivalence Rule

Answer 19

(p ↔ q) ꞉꞉ ((p → q) ⦁ (q → p))

p ↔ q) ꞉꞉ ((p ⦁ q) ᵥ ( ̴p ⦁ ̴q)

Question 20

Material Implication (MI)
Equivalence Rule

Answer 20

(p → q) ꞉꞉ ( ̴p ᵥ q)