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Math Help - p and q logic proof

  1. #1
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    p and q logic proof

    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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  2. #2
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    Using a truth table.
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  3. #3
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    (P↔Q) → (Q ↔R)

    and

    Q → (昱 → 星)
    These formulas are not equivalent: consider P = Q = False and R = True.
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  4. #4
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    Quote Originally Posted by cdoil View Post
    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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