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State whether the following statement is true or false? Give reasons for your answer.
Every rational number is an integer.___
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Question

State whether the following statement is true or false? Give reasons for your answer.
Every rational number is an integer.___

Answer

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Solution

A number that can be represented in the form \(\frac pq\), where \(p,q\) are integers and \(q\ne 0\) is called a rational number.
All the integers can be represented in the form of \(\frac p1\) where \(p\) is an integer and \(q=1\).
So, all the integers are rational numbers.
But all the rational numbers are not integers.
For example: \(\frac12\) is a rational number but it is not an integer.
Hence, the given statement is false.
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