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

Alisa plays with her dog in the yard when the weather is nice.

Short Answer

Expert verified

The hypothesis is 鈥渢he weather is nice鈥 and the conclusion is 鈥淎lisa plays with her dog in the yard鈥. The required if-then statement is 鈥淚f the weather is nice, then Alisa plays with her dog in the yard.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lisa plays with her dog in the yard when the weather is nice鈥.

03

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, 鈥渢he weather is nice鈥 and 鈥淎lisa plays with her dog in the yard鈥.

Note that the weather is nice does not depend on Alisa playing with her dog. However, Alisa playing with her dog is dependent on the weather being nice.

So, 鈥渢he weather is nice鈥 is the independent part of the statement and thus, the hypothesis. Similarly, 鈥淎lisa plays with her dog in the yard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 the weather is nice, then Alisa plays with her dog in the yard.鈥

This is the required if-then statement.

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