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Chapter 2: Q56. (page 80)

Write a counterexample for each conditional statement. (Lesson 1-8)

If the product of two numbers is an even number, then both factors must be even numbers.

Short Answer

Expert verified

The product of 2 and 3 is 6, which is even, but the factor 3 is not an even number.

Step by step solution

01

Step 1. Given information,

The given conditional statement is 鈥樷�� If the product of two numbers is an even number, then both factors must be even numbers鈥欌��.

02

Step 2. Concept used.

If the product of two numbers 2 and 3 then you will get 6 is an even number.

But 3 is not an even number.

It means, it is not always true that if the product of two numbers is an even number then both factors must be even numbers.

03

Step 3. To find the Counterexample of the given statement.

The Counterexample of the given Conditional Statement is 鈥淭he product of 2 and 3 is 6, which is even, but the factor 3 is not an even number鈥�.

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