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

• Maddie@sh.itjust.works ⁨5⁩ ⁨months⁩ ago

  Also no.

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  • Lafari@lemmy.world ⁨5⁩ ⁨months⁩ ago

    Thanks. Could you possibly elaborate? Why are they not equal?

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    • Boinkage@lemmy.world ⁨5⁩ ⁨months⁩ ago

      Substitute common sense terms. If I say “if it is an apple, it is a fruit”, does it then follow that a thing is a fruit if and only if it is an apple? No.

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      • Rhynoplaz@lemmy.world ⁨5⁩ ⁨months⁩ ago

        Better read that one again.

        “If B then A” … “B if and only if A”?

        If Apple then fruit. Is Apple ONLY if it’s a fruit.

        This one actually checks out.

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• Thoth19@lemmy.world ⁨5⁩ ⁨months⁩ ago

  No. They are effectively the same statement.

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

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  • Rhynoplaz@lemmy.world ⁨5⁩ ⁨months⁩ ago

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

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    • Casey_Masterpiece@lemmy.world ⁨5⁩ ⁨months⁩ 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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      • Rhynoplaz@lemmy.world ⁨5⁩ ⁨months⁩ ago

        But they switched the order in only the second half of the statement. I don’t know if everyone commenting caught that.

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    • Thoth19@lemmy.world ⁨5⁩ ⁨months⁩ 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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      • Rhynoplaz@lemmy.world ⁨5⁩ ⁨months⁩ ago

        Oh yeah. I was very confused as to what that meant, but I learned something today.

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  • zenharbinger@lemmy.world ⁨5⁩ ⁨months⁩ ago

    Also, Not (A XOR B)

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