Converse implication

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Converse 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:

p⊂q, Bpq, or p←q

Definition[edit]

Truth table[edit]

The truth table of A⊂B

a b
T T T
T F T
F T F
F F T

Venn diagram[edit]

The Venn diagram of "If B then A" (the white area shows where the statement is false)

Venn1101.svg

Properties[edit]

truth-preserving: The interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true' as a result of converse implication.

Symbol[edit]

Natural language[edit]

"Not q without p."

"p if q."

Boolean Algebra[edit]

(A + B')

See also[edit]