Question

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

The hypothesis is “the weather is nice” and the conclusion is “Alisa plays with her dog in the yard”. The required if-then statement is “If the weather is nice, then Alisa plays with her dog in the yard.”

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

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, “the weather is nice” and “Alisa plays with her dog in the yard”.

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, “the weather is nice” is the independent part of the statement and thus, the hypothesis. Similarly, “Alisa plays with her dog in the yard” 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 the weather is nice, then Alisa plays with her dog in the yard.”

This is the required if-then statement.