Q9. - Algebra 1

Question

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

If a number is a multiple of 10, then the number is divisible by 5.

The number is 955.

Step-by-Step Solution

Answer

There is no valid conclusion for the given statement and the given condition.

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 a number is a multiple of 10, then the number is divisible by 5”. The given condition is “the number is 955”.

Step 3. Identify the hypothesis and conclusion.

The given statement is an if-then statement. Then, the hypothesis is “a number is a multiple of 10” and the conclusion is “the number is divisible by 5”.

Step 4. Form a valid conclusion.

The given condition is “the number is 955”.

Note that 955 is not a multiple of 10, which implies that the hypothesis is false.

However, 955 is divisible by 5. So, the conclusion is true.

So, there is no valid conclusion.