Implications.
An implication or conditional is a molecular statement of the form
\begin{equation*}
P \imp Q
\end{equation*}
where \(P\) and \(Q\) are statements. We say that
\(P\) is the hypothesis (or antecedent).
\(Q\) is the conclusion (or consequent).
An implication is true provided \(P\) is false or \(Q\) is true (or both), and false otherwise. In particular, the only way for \(P \imp Q\) to be false is for \(P\) to be true and \(Q\) to be false.