• Thoth19
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    1 year ago

    No. They are effectively the same statement.

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

    • Rhynoplaz
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      1 year ago

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

      • Casey_Masterpiece
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        1 year 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.

        • Rhynoplaz
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          1 year ago

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

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

          This IS different from the original question.

      • Thoth19
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        1 year 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

        • Rhynoplaz
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          1 year ago

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

          • Thoth19
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            1 year 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