GenMath Logic

Question 1

Tautology.
[(P v Q) v R) → [P v (Q v R)]
[(P ^ Q) ^ R) → [P ^ (Q ^ R)]

Answer 1

Associative

Question 2

Tautology.
(P ^ Q) → (Q ^ P)
(P v Q) → (Q v P)

Answer 2

Commutative

Question 3

Tautology.
[(P v Q) ^ R) → [(P ^ R) v (Q ^ R)]
[(P ^ Q) v R) → [(P v R) ^ (Q v R)}]

Answer 3

Distributive

Question 4

Tautology.
[(P → Q) ^ (Q → P) ^ (Q → P)] → (P ↔ Q)]

Answer 4

Law of Biconditional Propositions

Question 5

Tautology.
[P ^ (P → Q)] → Q

Answer 5

Modus Ponens

Question 6

Tautology.
[(~Q ^ (P → Q)] → ~P

Answer 6

Modus Tollens

Question 7

Tautology.
[(P ^ Q) → R] → [P → (Q → R)]

Answer 7

Exportation

Question 8

Tautology.
(P → Q) → (~Q → ~P)

Answer 8

Transposition or Contraposition

Question 9

Tautology. P → (P v Q)

Answer 9

Addition

Question 10

Tautology. (P ^ Q) → P

Answer 10

Simplification

Question 11

Tautology. [(P) ^ (Q)] → (P ^ Q)

Answer 11

Conjunction

Question 12

Tautology. P → ~(~P)

Answer 12

Double Negation

Question 13

Tautology. (P → Q) → [P → (P ^ Q)]

Answer 13

Absorption

Question 14

Tautology. [(P v Q) ^ ~P] → Q

Answer 14

Disjunctive Syllogism

Question 15

Tautology. (P → Q) → (~P v Q)

Answer 15

Material Implication

Question 16

Tautology. (P v P) → P

Answer 16

Disjunctive Simplification

Question 17

Tautology. (P V Q) ^ (~P v R) → (Q v R)

Answer 17

Resolution

Question 18

Tautology.
[(P → Q) ^ (Q ^ R)] → (P → R)

Answer 18

Hypothetical Syllogism

Question 19

Tautology.
[(P → Q) ^ (R → S)] ^ (P v R) → (Q v S)

Answer 19

Constructive Dilemma

Question 20

Tautology.
[(P → Q) ^ (R → S)] ^ (~Q v ~S) → ~P v ~R)

Answer 20

Destructive Dilemma

Question 21

Valid Arguments.
P → Q
P
———-
∴ Q

Answer 21

Direct Reasoning or Modus Ponens

Question 22

Valid Arguments.
P → Q
~Q
———-
∴ ~P

Answer 22

Contrapositive Reasoning or Modus Tolens

Question 23

Valid Arguments.
P v Q ____________ P v Q
~P ________________~Q
——- ____________———–
∴ Q_______________ ∴ P

Answer 23

Disjunctive Reasoning or Disjunctive Syllogism

Question 24

Valid Arguments.
P → Q
Q → R
————–
∴ P → R
~R → ~P

Answer 24

Transitive Reasoning or Hypothetical Syllogism

Question 25

Fallacy.
P → Q
Q
————
∴ P

Answer 25

Fallacy of the Converse

Question 26

Fallacy.
P → Q
~P
———–
∴ ~Q

Answer 26

Fallacy of the Inverse

Question 27

Fallacy.
P v Q ________________ P v Q
P ____________________ Q
———— ____________ ————-
∴ ~Q _________________ ∴ ~P

Answer 27

Misuse of Disjunctive Reasoning

Question 28

Fallacy.
P → Q
Q → R
———————-
∴ R → P
~P → ~R

Answer 28

Misuse of Transitive Reasoning