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Q.

State true or false. Every integer is a rational number but every rational number need not be an integer.

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a

True

b

False

answer is A.

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Detailed Solution

To check whether the given statement holds or not.
An integer in a number system is defined as a number without any fractional part and it can be either positive or negative.
Next, a rational number is the one which can be expressed as a fraction or a ratio of two integers say

p q

, where p and q are both integers and q is always non-zero.
So, from these two definitions, it is understood that all such rational numbers which have a fractional part or in other words, a denominator other than 1, can never be called an integer.
For example,

42

can be simplified as

21

or just 2, which is an integer.
But if we consider its reciprocal, i.e.,

12

, then we can observe it is a fraction and not an integer.
Hence, the statement is true. Hence the correct option is (1).

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