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Biconditional versus identity

  1. Jun 10, 2008 #1
    Suppose we have a statement A that holds if and only if statement B holds.

    "A if and only if B"

    I'm fairly sure I read before that this does not necessarily mean that A and B are identical: in general, A <--> B does not imply A = B.

    I'm having difficulty determining how A and B could be distinguished from each other - besides, of course, their names.

    I think that a simple, concrete example would clear this up for me; if someone could provide one I'd greatly appreciate it. My sanity's been really wearing thin, lately (just have a look at my other thread; actually, don't)... maybe I should lay off the Red Bulls.
  2. jcsd
  3. Jun 10, 2008 #2

    matt grime

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    _Equality_ of logical statements doesn't really make sense. But if you still want an example:

    Let n be an integer, then n is even if and only if n^2 is even.

    It doesn't make sense to say (n is even) equals (n^2 is even), unless you wish to define what you mean by 'equal'. The two statements are equivalent, in the obvious sense.
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