## FANDOM

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In propositional logic and various other logics, the Material Conditional is the logical connective and binary truth operation represented symbolically as $P \to Q$ and outputs false whenever $P$ is true and $Q$ is false. They are often expressed in natural language as a condtional sentence, even though they often differ in function from indictive conditionals.

## Truth tableEdit

$P \to Q$ $P$ $Q$
$\top$ $\top$ $\top$
$\top$ $\bot$ $\top$
$\bot$ $\top$ $\bot$
$\top$ $\bot$ $\bot$

## InverseEdit

If $P \to Q is$ is a material conditional, then $\lnot P \to \lnot Q$ is the inverse of $P \to Q$.

## ConverseEdit

If $P \to Q$ is a material conditional, then $Q \to P$ is the converse of $P \to Q$.

## TranspositionEdit

If $P \to Q$ is a material conditional, then $\lnot Q \to \lnot P$ is the transpositive of $P \to Q$.