Exclusive Or -Logic Find a formula using only the connectives: conjunction, disjunction, and negation that is equivalent to,   P exclusive or Q. I cannot figure out a way to come up with a logical equivalent statement without randomly guessing.

We have:
$$\lnot ((P \land Q) \lor (\lnot P \land \lnot Q))$$
and:
$$(P\lor Q)\land (\lnot P \lor \lnot Q)$$
From the comments:
$$(P\lor Q) \land \lnot(P \land Q)$$
addendum: adding lemontree's for completeness:
$$(P \land \lnot Q) \lor (\lnot P \land Q))$$
