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Question

Which of the following statements are true and which are false?
(i) Every whole number is a rational number.
(ii) Every integer is a rational number.
(iii) 0 is a whole number but it is not a rational number.

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Solution

1. True
A whole number can be expressed as ab, with b=1 and a0. Thus, every whole number is rational.

2. True
Every integer is a rational number because any integer can be expressed as ab, with b=1 and 0>a0. Thus, every integer is a rational number.

3. False
0=ab, for a=0 and b0. Thus, 0 is a rational and whole number.

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