Question

Which of the following is a null set?

(a) {x : x is a natural number and x^2=4}

(b) {x : x is a rational number and x^2=2}

(c) {x : x is an even prime number}

(d) {x : x is name of the day of week}

I have been asked this question in an interview.

The origin of the question is The Empty Set in section Sets of Mathematics – Class 11

Answer 1

Correct answer is (b) {x : x is a rational number and x^2=2}

Explanation: x^2=4 => x=2,-2 where 2 is a natural number so X={2}.

X={2} for even prime number. Also we have seven days of the week so they cannot form null set.

x^2=2 => x=√2, -√2 they both are irrational so, it is a null set.