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
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 & Mackworth, 2017, sec. 5.1)
Construct the truth table for the statement
\[\begin{equation*}
P \implies Q \> \equiv \> \lnot P \lor Q.
\end{equation*}
\]
<<scheme/org-truth-table>>
(org-truth-table (lambda (p q) (or (not p) q))
'("P" "Q" "P \\implies Q"))
| \(P\) | \(Q\) | \(P \implies Q\) |
|---|---|---|
| false | false | true |
| false | true | true |
| true | false | false |
| true | true | true |