Question

Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by 5;
(ii) Set of all even prime numbers;
(iii) {x : x² −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) All natural numbers that end with 0 are even & divisible by 5. Therefore, the given set is not an example of empty set.
(ii) 2 is an even prime number. Therefore, the given set is not an example of empty set.
(iii) There is no rational number whose square is 2 such that x²$-$2 = 0. Therefore, it is example of empty set.
(iv) It is not possible that x$<$8 and, at the same time, x$>12$. Therefore, it is an example of empty set.
(v) There is no common point in two parallel lines. Therefore, it is an example of empty set.