Equivalent Statements: An Example

[samp]

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.

 

[matt grime]

_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.