Truth Conditions for Connectives.
\(P \wedge Q\) is true when both \(P\) and \(Q\) are true.
\(P \vee Q\) is true when \(P\) or \(Q\) or both are true.
\(P \imp Q\) is true when \(P\) is false or \(Q\) is true or both.
\(P \iff Q\) is true when \(P\) and \(Q\) are both true, or both false.
\(\neg P\) is true when \(P\) is false.