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

• Rhynoplaz@lemmy.world ⁨9⁩ ⁨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 ⁨9⁩ ⁨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 ⁨9⁩ ⁨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 ⁨9⁩ ⁨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 ⁨9⁩ ⁨months⁩ ago

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

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      • Thoth19@lemmy.world ⁨9⁩ ⁨months⁩ ago

        Yeah if vs iff can be confusing at first. Trying to understand it with normal grammar doesn’t work right. It’s a lot more helpful to grok the symbols and so the truth tables by hand to see how they fit together

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• zenharbinger@lemmy.world ⁨9⁩ ⁨months⁩ ago

  Also, Not (A XOR B)

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