Law of detachment

The law of detachment (also known as affirming the antecedent and Modus ponens) is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below:

1. P→Q (conditional statement)
2. P (hypothesis stated)
3. Q (conclusion deduced)

In deductive reasoning, we can conclude Q from P by using the law of detachment.^[3] However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no definitive conclusion.

The following is an example of an argument using the law of detachment in the form of an if-then statement:

1. If an angle satisfies 90°<A<180°, then A is an obtuse angle.
2. A=120°
3. A is an obtuse angle.

Since the measurement of angle A is greater than 90°, we can deduce that A is an obtuse angle.
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