Problem 148

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Every rational number is an integer.

Step-by-Step Solution

Verified
Answer
The statement 'Every rational number is an integer' is false. When amended to 'Every integer is a rational number', the statement is true.
1Step 1: Understand the Terminologies
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. An integer is a whole number that can be positive, negative, or zero.
2Step 2: Evaluate the Statement
Considering the definition of both rational numbers and integers, every integer (for instance, 5) can be expressed as a rational number (like 5/1), but not all rational numbers are integers (for example, 1/2). Therefore, the given statement is false.
3Step 3: Amend the Statement
To amend the statement to make it true, it can be reframed as: 'Every integer is a rational number'.