Q28. - Algebra 1

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 a $91\%$ on the exam.

Step-by-Step Solution

Answer

Since the hypothesis is true for the given statement and the given condition, there is no valid conclusion.

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 $91\%$ 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 $91\%$ on the exam”, which implies that the hypothesis is true.

Then if the conclusion is true, the statement must also be true. However, if the conclusion is false, then the statement will be false.

So, there is no valid conclusion for the given statement and the given condition.