Problem 149 - Algebra and Trigonometry

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some whole numbers are not integers.

Step-by-Step Solution

Answer

The statement, 'Some whole numbers are not integers,' is False. The corrected statement is 'All whole numbers are integers.'

Step 1: Understanding Definitions

Whole numbers are all non-negative numbers without any decimal point such as 0,1,2,3, etc. Integers include both negative and positive numbers without any decimal point such as -2,-1,0,1,2, etc, besides also including zero.

Step 2: Comparing Definitions

Since every whole number can be found in the set of integers, it can be said that all whole numbers are indeed integers. The difference is that integers include negative numbers and zero while whole numbers contain only positive numbers and zero.

Step 3: Evaluate the statement

The statement says 'Some whole numbers are not integers', which contradicts with what we established in step 2. So the statement is false.

Step 4: Correct the statement

To make the statement true, it should be revised to: 'All whole numbers are integers.' This statement reflects the proper relationship between whole numbers and integers.