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