Converse implication

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

Truth table

The truth table of A⊂B


a	b	⊂
T	T	T
T	F	T
F	T	F
F	F	T

Venn diagram

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

Properties

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.

Natural language

"Not q without p."

"p if q."

Boolean Algebra

(A + B')

Logical connectives

Tautology $\top$

NAND $\uparrow$ Converse implication $\leftarrow$ Implication $\rightarrow$ OR $\lor$

Negation $\neg$ XOR $\oplus$ Biconditional $\leftrightarrow$ Statement

NOR $\downarrow$ Nonimplication $\nrightarrow$ Converse nonimplication $\nleftarrow$ AND $\land$

Contradiction $\bot$

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