Converse nonimplication
Encyclopedia
In logic
, converse nonimplication is a logical connective
which is the negation
of the converse of implication
.
which is the same as 
of
.
of "It is not the case that B implies A" (the red area is true)
are
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, converse nonimplication is a logical connective
Logical connective
In logic, a logical connective is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the compound sentence produced has a truth value dependent on the respective truth values of the original sentences.Each logical connective can be expressed as a...
which is the negation
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
of the converse of implication
Implication
Implication may refer to:In logic:* Logical implication, entailment, or consequence, a relation between statements* Material implication, or conditional implication, a binary truth functionIn linguistics, specifically in pragmatics:...
.
Definition
which is the same as Truth table
The truth tableTruth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their...
of
.| p | q |  |
|---|---|---|
| T | T | F |
| T | F | F |
| F | T | T |
| F | F | F |
Venn diagram
The Venn DiagramVenn diagram
Venn diagrams or set diagrams are diagrams that show all possible logical relations between a finite collection of sets . Venn diagrams were conceived around 1880 by John Venn...
of "It is not the case that B implies A" (the red area is true)
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 nonimplicationSymbol
Alternatives for are
: 
combines Converse implication'sConverse implicationConverse implication is the converse of implication. That is to say; that for any two propositions P and Q, if Q implies P, then P is the converse implication of Q.It may take the following forms:-Truth table:The truth table of A⊂B-Venn diagram:...
left arrow(
) with Negation'sNegationIn logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
tilde(
).
: uses prefixed capital letter.
: 
combines Converse implication's left arrow(
) denied by means of a stroke(
).