Q30. - Algebra 1

Question

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 receives an A for the course.

Step-by-Step Solution

Answer

Since the conclusion is true for the given statement and the given condition and the hypothesis may or may not be true, 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 receives an A for the course”.

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 receives an A for the course”, which implies that the conclusion is true.

Now, even if the statement is true, the hypothesis may or may not be true. A student scoring less than $90\%$ may also receive an A for the course.

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