Conditional
A binary logical connective, denoted
\begin{equation*} P \implies Q \qor Q \impliedby P \end{equation*}where | \(P\) | is the antecedent |
\(Q\) | is the consequent, |
and read
“if \(P\), then \(Q\)” | |
or | “\(Q\) if \(P\)” |
or | “\(P\) implies \(Q\)”, |
that is true
if and only if
\(P\) and \(Q\) are true
or \(P\) is false
,
so equivalent to
\begin{equation*} \lnot P \lor Q. \end{equation*}Equivalent to its contrapositive but not to its converse.
(Levin 2021, sec. 0.2; Poole and Mackworth 2017, sec. 5.1)