Q49. - Algebra 1

Question

OPEN-ENDED Write a conditional statement. Write a counterexample to the statement. Explain your reasoning.

Step-by-Step Solution

Answer

The conditional statement is “If a number is prime, then it is odd.” The counterexample to this statement is when the number is 2.

Step 1. State the concept.

A conditional statement is usually written in an if-then format. The part of the statement following “if” is the hypothesis and the part of the statement following “then” is the conclusion.

A counterexample to a conditional statement is a case for which the hypothesis is true but the conclusion is false.

Step 2. List the objective.

The objective is to write a conditional statement and to write a counterexample to the statement.

Step 3. Write the conditional statement.

Let the conditional statement be “If a number is prime, then it is odd”.

Then the hypothesis is “a number is prime” and the conclusion is “it is odd”.

Step 4. Write a counterexample.

A counterexample to the conditional statement is when the number is 2.

Since 2 is a prime number, the hypothesis is true.

However, since 2 is an even number, it is not odd. Thus, the conclusion is false.