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Chapter 0: Problem 148

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.

Short Answer

Expert verified
The statement 'Every rational number is an integer' is false. When amended to 'Every integer is a rational number', the statement is true.

Step by step solution

01

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.
02

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.
03

Amend the Statement

To amend the statement to make it true, it can be reframed as: 'Every integer is a rational number'.

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