How do you FIND (not prove) an expression that is logically equivalent to another expression?

Question

I need to find an expression that is logically equivalent to q ↔ (¬p ∨ ¬q). I have already constructed a truth table for the expression, but it hasn't helped so I'm still unsure on how to find a logically equivalent expression. The truth table has given this output:

F F T F

Thanks for your help!

Answer 1

Your truth table indicates that your expression is true in exactly one of the four cases. That says that this expression is equivalent to one of $p \wedge q$, ${\lnot} p \wedge q$, $p \wedge {\lnot q}$, $\lnot p \wedge \lnot q$: I'll leave it to you to see which one.