Concept explainers
The statement of an indirect proof.
Explanation of Solution
Given information:
Amber and raquel are trying to verify the following statement using indirect proof. Is either of them correct? Explain your reasoning.
If the sum of two numbers is even, then the numbers are even.
Calculation:
Neither student is correct. Amber is incorrect because she doesn’t find a counter example to prove the statement false. Zero is not considered to be even or odd number so the example doesn’t meet the conditions of the hypothesis. Raquel is incorrect, as well. Although she comes up with a good counterexample to the statement, she makes the wrong conclusion that the statement is true.
So, the hypothesis is true when the conclusion is false, the statement is false.
Chapter 5 Solutions
Geometry, Student Edition
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