Material nonimplication or abjunction () is a term referring to a logic operation used in generic circuits and Boolean algebra. It is the negation of material implication. That is to say that for any two propositions is true if and only if is false.

, or "Lpq" (in Bocheński notation.

Definition

Truth table

Logical equivalences

Material nonimplication may be defined as the negation of material implication.In classical logic, it is also equivalent to the negation of the disjunction, and also the conjunction

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.

Symbol

The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 219B16 (8603 decimal): ↛.

Natural language

Grammatical

"p minus q."

"p without q."

Rhetorical

"p but not q."

"q is false, in spite of p."

Computer science

Bitwise operation: P & ~Q. This is usually called "bit clear" (BIC) or "and not" (ANDN).

Logical operation: P && !Q.

See also

• Implication

• Set difference

References

External links