Problem 149 - College Algebra Essentials

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 is false. A correct version of the statement: 'All whole numbers are integers.'

Step 1: Understanding the Concepts of Whole Numbers and Integers

Whole numbers include all natural numbers starting from zero (e.g.: 0, 1, 2, 3,...). On the other hand, integers include all natural numbers, their negatives, and zero (e.g.: ..., -3, -2, -1, 0, 1, 2, 3,...).

Step 2: Compare Whole Numbers with Integers

Once we understand what whole numbers and integers are, it's clear that all whole numbers are included in the set of integers. The difference is that integers also include negative numbers, which aren't included in whole numbers.

Step 3: Conclude on the Statement

Since every whole number falls within the set of integers, saying that 'Some whole numbers are not integers' is a false statement. A correction to make the statement true would be: 'All whole numbers are integers.'