Q21. - Algebra 1

Question

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.

Step-by-Step Solution

Answer

The hypothesis is “class is over” and the conclusion is “Joe will go to the mall”. The required if-then statement is “If a class is over, then Joe will go to the mall.”

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 “Joe will go to the mall after class”. This is equivalent to writing “Joe will go to the mall when class is over.”

Step 3. Identify the hypothesis and conclusion.

The given statement has two parts, “class is over” and “Joe will go to the mall”.

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, “class is over” is the independent part of the statement and thus, the hypothesis. Similarly, “Joe will go to the mall” 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 class is over, then Joe will go to the mall.”

This is the required if-then statement.