Question

Which of the following are examples of empty set ?

(i) Set of all even numbers divisible by 5.

(ii) Set of all even prime numbers.

(iii) {$x:x^2=0$ and x is rational}.

(iv) {x : x is a natural number, x < 8 and simultaneously x > 12}.

(v) {x : x is a point common to any two parallel lines}.

Answer 1

(i) This set is non-empty as 10 is an even natural number divisible by 5.

(ii) As 2 belongs to this set, so it is non-empty.

(iii) $x^2-2=0\Rightarrow x^2=2\Rightarrow x=\pm \sqrt{2}ϵQ$ , the set of rational numbers So, this set is empty.

(iv) This set is empty as there is no natural number x such that x < 8 and simultaneously x > 12.

(v) This set is empty as any two parallel lines never intersect each other.