Logic and Deductive Reasoning
Another frequently used law of logic is the Law of Syllogism. This is analogous to the transitive property of equality.
Law of Syllogism
If p implies q and q implies r, then p implies r.
Example
Form a logical conclusion using deductive reasoning based on the given statements.
| 1. |
If two angles form a linear pair, then they are supplementary. If two angles are supplementary, then the sum of their measures is 180°. |
| 2. |
Line m is parallel to line n. Line n is parallel to line s. |
Solution
Using the Law of Syllogism, you can form the following valid conclusions:
| 1. | If two angles form a linear pair, then the sum of their measures is 180°. |
| 2. | Line m is parallel to line s. |
