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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

Expert verified

The hypothesis is 鈥渁 number is only divisible by one and itself鈥 and the conclusion is 鈥渋t is prime鈥. The required if-then statement is 鈥淚f a number is only divisible by one and itself, then it is prime.鈥

Step by step solution

01

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 鈥渋f鈥 is the hypothesis, and the part of the statement immediately following 鈥渢hen鈥 is the conclusion.

02

Step 2. List the given data.

The given statement is 鈥淎 prime number is only divisible by one and itself鈥.

03

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, 鈥渁 number is only divisible by one and itself鈥 and 鈥渋t is prime鈥.

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

So, 鈥渁 number is only divisible by one and itself鈥 is the independent part of the statement and thus, the hypothesis. Similarly, 鈥渋t is prime鈥 is the dependent part of the statement and thus, the conclusion.

04

Step 4. Rewrite as an if-then statement.

Write the hypothesis after 鈥渋f鈥 and conclusion after 鈥渢hen鈥 in an if-then statement to get:

鈥淚f a number is only divisible by one and itself, then it is prime.鈥

This is the required if-then statement.

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