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 or p←q

Contents 1 Definition 1.1 Truth table 1.2 Venn diagram 2 Properties 3 Symbol 4 Natural language 4.1 Grammatical 4.2 Rhetorical 4.3 Colloquial 5 Boolean Algebra 6 Computer Science 7 See also

[edit] Definition

[edit] Truth table

The truth table of p⊂q

p	q	⊂
T	T	T
T	F	T
F	T	F
F	F	T

[edit] Venn diagram

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

[edit] 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.

[edit] Symbol

[edit] Natural language

[edit] Grammatical

[edit] Rhetorical

"Not q without p."

[edit] Colloquial

[edit] Boolean Algebra

[edit] Computer Science

[edit] See also

• Logical connective
• Material implication

v • d • e Logical connectives Tautology (⊤) OR (∨) · Converse implication (←) · Material implication (→) · NAND (↑) Proposition · XOR (⊕) · XNOR (↔) · Negation (¬) AND (∧) · Material nonimplication (↛) · Converse nonimplication (↚) · NOR (↓) Contradiction (⊥)