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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.<ref>Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004</ref> In some contexts, the consequent is called the apodosis.<ref>See Conditional sentence.</ref>
Examples:
- If <math>P</math>, then <math>Q</math>.
<math>Q</math> is the consequent of this hypothetical proposition.
- If <math>X</math> is a mammal, then <math>X</math> is an animal.
Here, "<math>X</math> 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".