Logical implication

The logical implication and the material conditional are both associated with an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if the first operand is true and the second operand is false.

The truth table associated with the material conditional if p then q (symbolized as p → q) and the logical implication p implies q (symbolized as p ⇒ q) is as follows:

Logical Implication

p	q	p ⇒ q
F	F	T
F	T	T
T	F	F
T	T	T

See also

Logical operators

Exclusive disjunction Logical conjunction Logical disjunction Logical equality

Logical implication Logical NAND Logical NNOR Negation

Related topics

Ampheck Boolean algebra Boolean domain Boolean function

Boolean logic Laws of Form Logic gate Logical graph

Peirce's law Propositional calculus Sole sufficient operator Zeroth order logic

Aficionados

• See Talk:Logical implication for discussions/comments regarding this article.
• See Logical implication/Aficionados for those who have listed Logical implication as an interest.
• See Talk:Logical implication/Aficionados for discussions regarding this interest.

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