Logical Proofs - Valid Implicational Arguments

Question 1

p ⊃ q
p
/∴ q

Answer 1

Modus Ponens (MP)

Question 2

Modus Ponens (MP)

Answer 2

p ⊃ q
p
/∴ q

Question 3

p ⊃ q
~ q
/∴ ~ p

Answer 3

Modus Tollens (MT)

Question 4

Modus Tollens (MT)

Answer 4

p ⊃ q
~ q
/∴ ~ p

Question 5

p ⊃ q
q
/∴ p

Answer 5

Affirming the Consequent (Invalid because it has a counter-example)

Question 6

Affirming the Consequent - (This is invalid because it has a counter-example)

Answer 6

p ⊃ q
q
/∴ p

Question 7

p ⊃ q
~p
/∴ ~ q

Answer 7

Denying the Antecedent (Invalid - has a counter-example)

Question 8

Denying the Antecedent (Invalid - has a counter-example)

Answer 8

p ⊃ q
~p
/∴ ~ q

Question 9

p ∨ q
~p
/∴ q

Answer 9

Disjunctive Syllogism (DS)

Question 10

Disjunctive Syllogism (DS)

Answer 10

p ∨ q
~p
/∴ q

Question 11

p ⊃ q
q ⊃ r
/∴ p ⊃ r

Answer 11

Hypothetical Syllogism (HS)

Question 12

Hypothetical Syllogism (HS)

Answer 12

p ⊃ q
q ⊃ r
/∴ p ⊃ r

Question 13

p . q
/ ∴ q

p . q
/ ∴ p

Answer 13

Simplification (Simp)

Question 14

Simplification (Simp)

Answer 14

p . q
/ ∴ q

p . q
/ ∴ p

Question 15

p
q
/ ∴ p . q

Answer 15

Conjunction (Conj)

Question 16

Conjunction (Conj)

Answer 16

p
q
/ ∴ p . q

Question 17

p
/ ∴ p v q

Answer 17

Addition (Add)

Question 18

Addition (Add)

Answer 18

p
/ ∴ p v q

Question 19

p ∨ q
p ⊃ r
q ⊃ s
/ ∴ r ∨ s

Answer 19

Constructive Dilemma (CD)

Question 20

Constructive Dilemma (CD)

Answer 20

p ∨ q
p ⊃ r
q ⊃ s
/ ∴ r ∨ s

Question 21

Implicational rules

Answer 21

One directional, only goes that one way

Question 22

Rules of Implication ______ be used with a single part of a statement

Answer 22

CAN NOT