Comment on Is "If A then B" equal to "B if and only if A"?

Maddie@sh.itjust.works ⁨2⁩ ⁨years⁩ ago

• Lafari@lemmy.world ⁨2⁩ ⁨years⁩ ago

  Is “If B then A” equal to “B if and only if A”?

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  • Thoth19@lemmy.world ⁨2⁩ ⁨years⁩ ago

    No. They are effectively the same statement.

    (A <=> B ) = (A=>B AND B=> A)

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    • Rhynoplaz@lemmy.world ⁨2⁩ ⁨years⁩ ago

      Wait. If they are effectively the same statement, wouldn’t that mean they ARE equal?

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      • Casey_Masterpiece@lemmy.world ⁨2⁩ ⁨years⁩ ago

        If B then A is the same as if X then Y is the same as if A then B. They are saying it’s the same as the OP. Changing the letters around doesn’t change the meaning since the letters are just placeholders.

        Now if you said If A then B AND If B then A as one it wouldn’t be the same because A and B would have to keep the same meaning.

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      • Thoth19@lemmy.world ⁨2⁩ ⁨years⁩ ago

        I mean it is the definition of “if and only if”. And by commutativity we also know that A iff B is equal to B iff A

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    • zenharbinger@lemmy.world ⁨2⁩ ⁨years⁩ ago

      Also, Not (A XOR B)

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