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


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


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


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

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