Material nonimplication
Logical connective
- 1 min read
- 5 chapters
Related on Lably
Through Boolean algebra, Proposition and If and only if
It may be written using logical notation as , , or "Lpq" (in Bocheński notation), and is logically equivalent to , and .
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 of and , and also the conjunction of and
Sign in to keep reading
4 more chapters are free with a Lably account.
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.