State true or false.

Between two rational numbers, there exists only one rational number.

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True

false

answer is B.

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Detailed Solution

It is given that between two rational numbers, there exists only one rational number.
Consider

a and b

as rational numbers. Then a rational number

n_{1}

can be find in between

a and b

such that

a < n_{1} < b

using the formula

n_{1} = \frac{a + b}{2}

.
Similarly, again we can find a rational number between

a and n_{1}

and

n_{1} and b

and so on.
Hence, between any two distinct rational numbers there are infinitely many rational numbers.
Therefore, the given statement is false.
Thus, option 2 is correct.

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