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A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the antecedent and Q is called the consequent.^[1] In some contexts, the consequent is called the apodosis.^[2]

Examples:

If $P$ , then $Q$ .

$Q$ is the consequent of this hypothetical proposition.

If $X$ is a mammal, then $X$ is an animal.

Here, " $X$ is an animal" is the consequent.

If computers can think, then they are alive.

"They are alive" is the consequent.

The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent.

If monkeys are purple, then fish speak Klingon.

"Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple.

References

^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004
^ See Conditional sentence.