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

Accepted Solution

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 thattwo 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                       TT     F         F        T             F             F                   T                       FF     T         T        F             F            T                   F                       FF     F         T        T             T            T                   T                       TSince 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).