Which of the following are examples of the null set? F = {x : x ϵ Q, – InterviewSolution

InterviewSolution

1.

Which of the following are examples of the null set? F = {x : x ϵ Q, 1 < x < 2}.

Answer»

Here, x ∈ Q

i.e. x is a rational number

We know that,

If a and b are two rational numbers, then \(\frac{a+b}{2}\) is a rational number between a and b such that a<\(\frac{a+b}{2}\) <b

So, the rational number 1 and 2 is

\(\frac{1+2}{2}\) = \(\frac{3}{2}\)

∴ the set is not empty

∴ It is not a null set.

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