Question

Which of the following sets are empty?
(i) A set of all even prime numbers,
(ii) B = {x|x is a capital of India}
(iii) F = {y}y is a point of intersection of two parallel lines}
(iv) G = {z|z $\in$N, 3 < z < 4}
(v) H = {t|t is a triangle having four sides

Answer 1

Empty set: A set is said to be empty or null if it has no element. It is denoted by $\mathrm{\varphi }$.

(i) A= {2}
This set contains 1 element. Therefore, it is not an empty set.

(ii) B= {Delhi}
This set contains 1 element. Therefore, it is not an empty set.

(iii) F={$\mathrm{\varphi }$}
As parallel lines never intersect each other, it is an empty set.

(iv) G={ $\mathrm{\varphi }$ }
This set does not contain any element, because no natural number is less than 4 but greater than 3.
Therefore, it is an empty set.

(v) H= {$\mathrm{\varphi }$}
A triangle has 3 sides. Thus, there exists no triangle which has 4 sides.
Therefore, it is an empty set.