Definition:Inverse Statement

Definition

The inverse of the conditional:

$p \implies q$

is the statement:

$\neg p \implies \neg q$

Also see

• Conditional and Inverse are not Equivalent: The inverse of a true conditional is not necessarily true, and the inverse of a false conditional is not necessarily false.

• Definition:Converse Statement
• Definition:Contrapositive Statement

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.14$: Application of laws of sentential calculus in inference
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Axioms