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Is "If A then B" equal to "B if and only if A"? (lemmy.world)
submitted 2 years ago by to c/nostupidquestions@lemmy.world
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[–] 3 points 2 years ago (2 children)

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

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  • [–] 2 points 2 years ago (1 child)

    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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  • [–] 2 points 2 years 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.

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  • [–] 1 point 2 years ago (1 child)

    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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  • [–] 2 points 2 years ago (1 child)

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

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  • [–] 1 point 2 years 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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