Use a truth table to show that P Qand (~PV Q) A (~QV P) are equivalen

Answer: The given logical equivalence is proved below.

Step-by-step explanation: We are given to use truth tables to show the following logical equivalence:

P ⇔ Q ≡ (∼P ∨ Q) ∧ (∼Q ∨ P)

We know that

two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.

The truth table is as follows:

P Q ∼P ∼Q P⇔ Q ∼P ∨ Q ∼Q ∨ P (∼P ∨ Q) ∧ (∼Q ∨ P)

T T F F T T T T

T F F T F F T F

F T T F F T F F

F F T T T T T T

Since the corresponding truth vales for P ⇔ Q and (∼P ∨ Q) ∧ (∼Q ∨ P) are same, so the given propositions are logically equivalent.

Thus, P ⇔ Q ≡ (∼P ∨ Q) ∧ (∼Q ∨ P).