Question

Example 3 Determine whether a valid conclusion follows from the statement below for each given condition. If a valid conclusion does not follow, write no valid conclusion and explain why.

If Belinda scores higher than $90\%$on the exam, then she will receive an A for the course.

Belinda scores an $89\%$on the exam.

Short answer

Since the hypothesis is false for the given statement and the given condition, the valid conclusion is that regardless of the conclusion being true or false, the statement must also be true.

Step-by-step solution

Step 1. State the concept.

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 “If Belinda scores higher than $90\%$ on the exam, then she will receive an A for the course”. The given condition is “Belinda scores a $89\%$ on the exam”.

Step 3. Identify the hypothesis and conclusion.

The given statement is an if-then statement. Then, the hypothesis is “Belinda scores higher than $90\%$ on the exam” and the conclusion is “she will receive an A for the course”.

Step 4. Form a valid conclusion.

The given condition is “Belinda scores a $89\%$ on the exam”, which implies that the hypothesis is false.

Then regardless of the conclusion being true or false, the statement is said to be true.

This is the valid conclusion for the given statement and the given condition.