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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.

Short Answer

Expert verified

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

Step by step solution

01

Step 1. State the concept.

In an if-then statement, the part of the statement immediately following 鈥渋f鈥 is the hypothesis, and the part of the statement immediately following 鈥渢hen鈥 is the conclusion.

02

Step 2. List the given data.

The given statement is 鈥淚f Belinda scores higher than 90% on the exam, then she will receive an A for the course鈥. The given condition is 鈥淏elinda scores a 91% on the exam鈥.

03

Step 3. Identify the hypothesis and conclusion.

The given statement is an if-then statement. Then, the hypothesis is 鈥淏elinda scores higher than 90% on the exam鈥 and the conclusion is 鈥渟he will receive an A for the course鈥.

04

Step 4. Form a valid conclusion.

The given condition is 鈥淏elinda scores a 91% on the exam鈥, 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.

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