Converse nonimplication

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

Contents 1 Definition 1.1 Truth table 1.2 Venn diagram 2 Properties 3 Symbol 4 Natural language 4.1 Grammatical 4.2 Rhetorical 4.3 Colloquial 5 Boolean algebra 6 Computer science 7 See also

[edit] Definition

p⊄q which is the same as ~(p ← q)

[edit] Truth table

The truth table of p ⊄ q.

p	q	⊄
T	T	F
T	F	F
F	T	T
F	F	F

[edit] Venn diagram

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

[edit] 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

[edit] Symbol

[edit] Natural language

[edit] Grammatical

[edit] Rhetorical

"not...but"

[edit] Colloquial

[edit] Boolean algebra

[edit] Computer science

[edit] See also

v • d • e Logical connectives Tautology (⊤) OR (∨) · Converse implication (←) · Material implication (→) · NAND (↑) Proposition · XOR (⊕) · XNOR (↔) · Negation (¬) AND (∧) · Material nonimplication (↛) · Converse nonimplication (↚) · NOR (↓) Contradiction (⊥)