Converse nonimplication
In logic, converse nonimplication is a logical connective which is the negation of converse implication.
Definition
Converse nonimplication is notated, or, and is logically equivalent to and.Truth table
The truth table of.Notation
Converse nonimplication is notated, which is the left arrow from converse implication, negated with a stroke.Alternatives include
- , which combines converse implication's, negated with a stroke.
- , which combines converse implication's left arrow with negation's tilde.
- Mpq, in Bocheński notation
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 converse nonimplicationNatural language
Grammatical
Example,If it rains then I get wet, just because I am wet does not mean it is raining, in reality I went to a pool party with the co-ed staff, in my clothes and that is why I am facilitating this lecture in this state.
Rhetorical
Q does not imply P.Colloquial
Not P, but Q.Boolean algebra
Converse nonimplication in a general Boolean [algebra (structure)|Boolean algebra] is defined as.
Example of a 2-element Boolean algebra: the 2 elements with 0 as zero and 1 as unity element, operators as complement operator, as join operator and as meet operator, build the Boolean algebra of propositional logic.
Example of a 4-element Boolean algebra: the 4 divisors of 6 with 1 as zero and 6 as unity element, operators as complement operator, as join operator and as meet operator, build a Boolean algebra.
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