In mathematical notation for conditionals, the Law of Detachment states:

Mediocre definition from your book: If p –> q is a true statement and *p* is true then *q *is true.

The way you usually encounter it in given problems:

If *p* –> *q *is a true statement, and Event A meets the conditions of *p*, then *q* must also have happened.

Also note, that if Event A only meets the conditions of *q*, then that does not mean that *p* happened or is true.

**How to use the Law of Detachment**

When you are given a statement, if it is not already in “If…, then…” form, rewrite it that way. Then represent it as a Venn Diagram. Consider the other information you are given. Does it occur with in the “*p*” part of the Venn Diagram, or only the “*q*” part? (Does it satisfy the *hypothesis *or the *conclusion*?) Then determine whether or not you can make a *valid* deduction or conjecture.

Get some practice by following this link to a great Khan Academy module. If you feel like you’re really getting it (10 or more correct in a row), check out any of the other “Logical Reasoning” modules by clicking on the other tabs on the left of the screen.

*Warning*: This module also makes use of the Law of Syllogisms, so make sure that you check that out before practicing.

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