Question

Example 2: Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.

6. A prime number is only divisible by one and itself.

Short answer

The hypothesis is “a number is only divisible by one and itself” and the conclusion is “it is prime”. The required if-then statement is “If a number is only divisible by one and itself, then it is prime.”

Step-by-step solution

Step 1. State the concept.

In a conditional statement, the independent part is the hypothesis and the dependent part is the conclusion.

In an if-then statement, the part of the statement immediately following “if” is the hypothesis, and the part of the statement immediately following “then” is the conclusion.

Step 2. List the given data.

The given statement is “A prime number is only divisible by one and itself”.

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, “a number is only divisible by one and itself” and “it is prime”.

Note that a number being prime depends on only being divisible by one and itself.

So, “a number is only divisible by one and itself” is the independent part of the statement and thus, the hypothesis. Similarly, “it is prime” is the dependent part of the statement and thus, the conclusion.

Step 4. Rewrite as an if-then statement.

Write the hypothesis after “if” and conclusion after “then” in an if-then statement to get:

“If a number is only divisible by one and itself, then it is prime.”

This is the required if-then statement.