Which of the following are examples of empty set?
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}.

Solution:

(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 $x^{2}-2=0$. 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.

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