Hello all. I am trying to prove (P↔Q) → (Q ↔R) and Q → (昱 → 星) are logically equivalent, by way of proof. Rules are DeMorgan's Laws may not be used. Any help is appreciated. Thanks.
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Using a truth table.
(P↔Q) → (Q ↔R) and Q → (昱 → 星) These formulas are not equivalent: consider P = Q = False and R = True.
Originally Posted by cdoil Hello all. I am trying to prove (P↔Q) → (Q ↔R) and Q → (昱 → 星) are logically equivalent, by way of proof. Rules are DeMorgan's Laws may not be used. Any help is appreciated. Thanks. [(P↔Q) → (Q ↔R)] logically implies [Q → (昱 → 星)] and hence provable. (meaning, by assuming [(P↔Q) → (Q ↔R)] we can prove [Q → (昱 → 星)] ) But [Q → (昱 → 星)] does logically implies [(P↔Q) → (Q ↔R)] and thus not provable
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