Logical Equivalence

Question 1

Identity Law 1

Answer 1

p ∧ T ≡ p

Question 2

Identity Law 2

Answer 2

p ∨ F ≡ p

Question 3

Domination Law 1

Answer 3

p ∨ T ≡ T

Question 4

Domination Law 2

Answer 4

p ∧ F ≡ F

Question 5

Idempotent Law 1

Answer 5

p ∨ p ≡ p

Question 6

Idempotent Law 2

Answer 6

p ∧ p ≡ p

Question 7

Double Negation Law

Answer 7

¬(¬p) ≡ p

Question 8

Negation Law 1

Answer 8

p ∨ ¬p ≡ T

Question 9

Negation Law 2

Answer 9

p ∧ ¬p ≡ F

Question 10

Commutative Law 1

Answer 10

p ∨ q ≡ q ∨ p

Question 11

Commutative Law 2

Answer 11

p ∧ q ≡ q ∧ p

Question 12

Associative Law 1

Answer 12

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Question 13

Associative Law 2

Answer 13

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

Question 14

Distributive Law 1

Answer 14

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Question 15

Distributive Law 2

Answer 15

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

Question 16

Absorption Law 1

Answer 16

p ∨ (p ∧ q) ≡ p

Question 17

Absorption Law 2

Answer 17

p ∧ (p ∨ q) ≡ p

Question 18

De Morgan’s Law 1

Answer 18

¬(p ∧ q) ≡ ¬p ∨ ¬q

Question 19

De Morgan’s Law 2

Answer 19

¬(p ∨ q) ≡ ¬p ∧ ¬q

Question 20

Conditional 1

Answer 20

p → q ≡ ¬p ∨ q

Question 21

Conditional 2

Answer 21

p → q ≡ ¬q → ¬p

Question 22

Conditional 3

Answer 22

p ∨ q ≡ ¬p → q

Question 23

Conditional 4

Answer 23

p ∧ q ≡ ¬(p → ¬q)

Question 24

Conditional 5

Answer 24

¬(p → q) ≡ p ∧ ¬q

Question 25

Conditional 6

Answer 25

(p → q) ∧ (p → r) ≡ p → (q ∧ r)

Question 26

Conditional 7

Answer 26

(p → r) ∧ (q → r) ≡ (p ∨ q) → r

Question 27

Conditional 8

Answer 27

(p → q) ∨ (p → r) ≡ p → (q ∨ r)

Question 28

Conditional 9

Answer 28

(p → r) ∨ (q → r) ≡ (p ∧ q) → r

Question 29

Biconditional 1

Answer 29

p ↔ q ≡ (p → q) ∧ (q → p)

Question 30

Biconditional 2

Answer 30

p ↔ q ≡ ¬p ↔ ¬q

Question 31

Biconditional 3

Answer 31

p ↔ q ≡ (p ∧ q) ∨ (¬p ∧ ¬q)

Question 32

Biconditional 4

Answer 32

¬(p ↔ q) ≡ p ↔ ¬q