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# State whether the following statement is true or false. Give reasons for your answer.Every rational number is a whole number[a] True.[b] False.

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Hint: In order to prove that a statement is incorrect, we have to come up with a counterexample, and in order to prove it correct, we have to come up with a formal proof. Recall the definitions of a rational number. Try finding a counterexample in the above case, i.e. find a rational number which is not a whole number.

Complete step-by-step answer:
Rational Numbers: Number which can be expressed in the form of \$\dfrac{p}{q}\$ where p and q are integers and \$q\ne 0\$ are called rational numbers.
Whole numbers: The numbers 0,1,2,…, are called whole numbers.
Consider the number \$\dfrac{3}{2}\$.
Since 2 and 3 are integers and 2 is non-zero, we have \$\dfrac{3}{2}\$ is a rational number.
But \$\dfrac{3}{2}\$ is not a whole number.
Hence there exists a rational number which is not a whole number.
Hence the claim that every rational number is a whole number is incorrect.
Hence option [b] is correct.

Note: [1] The method of proof, as done above, is called proof by counterexample.
[2] Every rational number is not a whole number, but every whole number is a rational number. This is because every whole number is an integer and every integer n can be expressed in the form \$\dfrac{n}{1}\$ and since n and 1 both are integers and 1 is non-zero, n is a rational number.