I am working on a problem where I need to show the logical equivalence of two propositions. One is a biconditional: $p \leftrightarrow q$. And the other is this: $(p \land q) \lor (\lnot p \land \lnot q)$
I can get the biconditional down to this: $(\lnot p \lor q) \land (\lnot q \lor p)$
And I don't know how to change the second proposition. Can someone give me a place to start?
Best Answer
$p$ iff $q$ is true precisely when either: (both $p$ and $q$ are true) or (both $p$ and $q$ are false).
This can be seen by just making truth tables. In any event, this is exactly the identity in question.