Conjunction and disjunction combine statements symmetrically, but implication introduces direction. The statement $p\to q$ says that the truth of $p$ leads to the truth of $q$. This direction is essential in definitions, theorems, proofs, algorithms, and everyday mathematical language. In this lesson, implication and biconditional will be studied through hypotheses, conclusions, necessary conditions, and sufficient conditions.

Let $p$ and $q$ be statements. The \textbf{implication} from $p$ to $q$ is denoted by $p\to q$ and is read as if $p$, then $q$.