Q8. - Algebra 1

Question

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 5010.

Step-by-Step Solution

Answer

The hypothesis and conclusion of the given statement are both true for the given condition. Thus, the given condition satisfies the given statement.

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 5010”.

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 5010”.

Note that 5010 is a multiple of 10, which implies that the hypothesis is true.

Moreover, 5010 is also divisible by 5. So, the conclusion is also true.

Thus, the given condition satisfies the given statement.