Material nonimplication
Material nonimplication or abjunction (latin ab = "from", junctio =–"joining") is the negation of material implication. That is to say that for any two propositions P and Q, the material nonimplication from P to Q is true if and only if not P implies Q. This is more naturally stated as that the material nonimplication from P to Q is true only if P is true and Q is false.
It may be written using logical notation as:
- p⊅q
- Lpq
- p↛q
And is equivalent to:
- p∧~q
Definition
Truth table
| p | q | ↛ |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |
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 8603 (decimal).
Natural language
Rhetorical
"p but not q."
Boolean algebra
(A'+B)'
Computer science
Bitwise operation: A&(~B)
Logical operation: A&&(!B)
See also
References
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