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Example 2 Identify the hypothesis and conclusion of each statement.

Then write each statement in if-then form.

Joe will go to the mall after class.

Short Answer

Expert verified

The hypothesis is 鈥渃lass is over鈥 and the conclusion is 鈥淛oe will go to the mall鈥. The required if-then statement is 鈥淚f a class is over, then Joe will go to the mall.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 鈥淛oe will go to the mall after class鈥. This is equivalent to writing 鈥淛oe will go to the mall when class is over.鈥

03

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, 鈥渃lass is over鈥 and 鈥淛oe will go to the mall鈥.

Note that the class being over does not depend on Joe going to the mall. However, Joe going to the mall is dependent on the class is over.

So, 鈥渃lass is over鈥 is the independent part of the statement and thus, the hypothesis. Similarly, 鈥淛oe will go to the mall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 class is over, then Joe will go to the mall.鈥

This is the required if-then statement.

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