# Law of Detachment

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 is true.

The way you usually encounter it in given problems:

If p –> 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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### 5 Responses to Law of Detachment

1. Alex Gayraud says:

Come to my water polo game 😀

2. taran meek says:

hey i have a football game today and if if you come , then i will be happy. i used a syllogism so i hope u can come

3. Alex Gayraud says:

hi 😛

4. Terrel Alexander says:

Hey Mr. Z this website is really helpful hank you so much for inspiring me to do better

5. Michael Kelker says:

Hey Mr Z 😀 😛 🙂 🙁 😉 :O