Material nonimplication

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material nonimplication is the negation of implication. p⊅q

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

[edit] Truth table

p	q	⊅
T	T	F
T	F	T
F	T	F
F	F	F

[edit] Venn diagram

The Venn Diagram of "It's not the case that A implies B" (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 material nonimplication.

[edit] Symbol

[edit] Natural language

[edit] Grammatical

[edit] Rhetorical

"It's not the case that p implies q."
"p but not q."

[edit] Colloquial

[edit] Boolean Algebra

[edit] Computer Science

[edit] See also

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