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In logic, converse nonimplication is a logical connective which is the negation of the converse of implication.

Definition

p⊄q which is the same as ~(p ← q)

Truth table

The truth table of p ⊄ q.

Venn diagram

The Venn Diagram of "It is not the case that B implies A" (the red area is true)

Properties

falsehood-preserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of converse nonimplication

Symbol

Natural language

Grammatical

Rhetorical

"not...but"

Colloquial

Boolean algebra

Computer science

See also

v • d • e Logical connectives Tautology OR · ← · → · NAND Proposition • XOR · XNOR • Negation AND · ↛ · ↚ · NOR Contradiction

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