Consequent
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Consequent

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 ${\displaystyle P}$, then ${\displaystyle Q}$.

${\displaystyle Q}$ is the consequent of this hypothetical proposition.

• If ${\displaystyle X}$ is a mammal, then ${\displaystyle X}$ is an animal.

Here, "${\displaystyle X}$ 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

1. ^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004
2. ^