Rules of Inference

Question 1

Answer 1

Modus Ponens

Question 2

Answer 2

Modus Tollens

Question 3

Answer 3

Hypothetical Syllogism (Transitivity)

Question 4

Answer 4

Disjunctive Syllogism

Question 5

Answer 5

addition

Question 6

Answer 6

Simplification

Question 7

Answer 7

Conjunction

Question 8

Answer 8

Resolution

Question 9

A declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.

Answer 9

Proposition

Question 10

p ^ q

Answer 10

conjunction

Question 11

p v q

Answer 11

disjunction

Question 12

converse, contrapositive, or inverse? p –> q, q –> p

Answer 12

converse

Question 13

converse, contrapositive, or inverse? p –> q, ¬q –> ¬p

Answer 13

contrapositive

Question 14

converse, contrapositive, or inverse? p –> q, ¬p –> ¬q

Answer 14

inverse

Question 15

A compound proposition that is always true, no matter what the truth values of the propositional variables that occur in it

Answer 15

tautology

Question 16

De Morgan’s Laws¬(p ^ q) ⌯ ¬p v ¬q, ¬(p v q) ⌯ ¬p ^ ¬q

Answer 16

De Morgan’s Laws

Question 17

Answer 17

Identity laws

Question 18

Answer 18

Domination laws

Question 19

Answer 19

Idempotent laws

Question 20

Answer 20

Double negation law

Question 21

Answer 21

Commutative law

Question 22

Answer 22

Associative laws

Question 23

Answer 23

Absorption laws

Question 24

Answer 24

Negation laws

Question 25

Answer 25

Universal instantiation

Question 26

Answer 26

Universal generalization

Question 27

Answer 27

Existential instantiation

Question 28

Answer 28

Existential generalization