Logic and Deductive Reasoning
Deductive reasoning uses laws of logic to form conclusions. One of the most often used laws in making formal arguments is presented below.
Law of Detachment
If "p implies q" is a true statement and p is true, then q is true.
Example
Use deductive reasoning to form a conclusion from the given statements.
| 1. |
If an angle is acute, then its measure is less than 90°. Angle A is acute. |
| 2. |
Two parallel lines do not intersect. Lines m and n are parallel. |
Solution
Since the given statement "p implies q" is true and the given premise p is true, then the conclusion q must be true. Using the Law of Detachment, the following conclusions are formed:
| 1. | The measure of angle A is less than 90°. |
| 2. | Lines m and n do not intersect. |
