# Honors Geometry Companion Book, Volume 1

2.1.3 Using Deductive Reasoning to Verify Conjectures (continued) Example 4 Applying the Laws of Deductive Reasoning

In this example, two conditionals are given to be true and the statement “Ed ran 10 miles on Monday” is also given to be true. A letter can be assigned to each statement in the two given conditionals to organize the statements. Applying the Law of Detachment to the first conditional results in the conclusion that the statement “Ed did not run the next day” is true. Since Tuesday is the day after Monday, the statement “Ed did not run on Tuesday” can also be assumed to be true. When the Law of Detachment is applied to this statement and the second given conditional, the result is that “Ed will run 10 miles on Wednesday” can be concluded. Therefore, if the Law of Detachment is applied twice to the given information, the conclusion “Ed will run 10 miles on Wednesday” must be true. Again, use the given information and the law of Detachment twice to reach a logical conclusion based on deductive reasoning.

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