From ProofWiki
Jump to navigation Jump to search


In a conditional $p \implies q$, the statement $q$ is the consequent.

Also known as

Some authors use the term conclusion for consequent, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ we reserve the use of conclusion for an element of the structure of a logical argument.

The term consequent clause can sometimes be seen, particularly when the conditional it is part of consists of a statement in natural language.

The archaic terms implicate and apodosis can sometimes be found.

Also defined as

Let $P = a \circ b$ be an expression.

The term $b$ is known as the consequent of $P$.

The term is usually applied when the expression in question is a ratio.

For example, in $5 : 7$, the number $5$ is the consequent.

Also see

  • Results about consequents can be found here.

Linguistic Note

The word consequent is usually found in classical mathematical literature, notably Euclid's The Elements.

The word comes from the Greek, and literally means following term.