Material nonimplication

Material nonimplication or abjunction (Latin ab = "away", junctio= "to join") is a term referring to a logic operation used in generic circuits and Boolean algebra.

is true if and only if the negation of the material implication from

This is more naturally stated as that the material nonimplication from

It may be written using logical notation as

, or "Lpq" (in Bocheński notation), and is logically equivalent to

In classical logic, it is also equivalent to the negation of the disjunction of

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.

The symbol for material nonimplication is simply a crossed-out material implication symbol.

"q is false, in spite of p." Bitwise operation: A & ~B.

This is usually called "bit clear" (BIC) or "and not" (ANDN).

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