3.4 Equivalent Statements

Question 1

Equivalent statements (symbolized ⇔ or ≡)

Answer 1

Two statements are equivalent if both statements have exactly the same truth values in answer columns of the truth tables

Question 2

Law 1 of DeMorgan’s laws for logic

Answer 2

~(𝑝 ∧ 𝑞) ⟺ ~𝑝 ∨ ~𝑞

Question 3

Law 2 of DeMorgan’s laws of logic

Answer 3

~(𝑝 ∨ 𝑞) ⟺ ~𝑝 ∧ ~𝑞

Question 4

How do you change a conditional statement to a disjunction?

Answer 4

Negate the antecedent (ex: p -> to ~p)
Change the conditional symbol to a disjunction symbol (ex: -> to V)
Keep the consequent the same (ex: -> q to the same)

Question 5

How do you change a disjunction to a conditional statement?

Answer 5

Negate the first statement (ex: p to ~p)
Change the disjunction symbol to a conditional symbol (ex: V to ->)
Keep the second statement the same

Question 6

Converse

Answer 6

p -> q to q -> p
(Equivalent to the inverse)

Question 7

Inverse

Answer 7

p -> q to ~p -> ~ q
(Equivalent to the converse)

Question 8

Contrapositive

Answer 8

p -> q to ~q -> ~p
(Equivalent to the conditional statement)