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:x 2 –2=0 and x is rational}. (iv) {x:x is a natural number, x 12}. (v) {x:x is a point common to any two parallel lines}.

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:x 2 –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}.

Philoid · Accepted Answer

Note: The Empty set is the set which does not contain any element. Most of the people get confused whether {0} is an empty set or not. It is not because it contains an element 0.

(i) All numbers ending with 0. Except 0 is divisible by 5 and are even. Hence it is not an example of empty set.

(ii) 2 is a prime number and is even, and it is the only prime which is even. So no this not an example of the empty set.

(iii) There is not natural number whose square is 2. So it is an example of empty set.

(iv) Never can a number be simultaneously less than 8 and greater than 12. Hence it is an example of the empty set.

(v) No two parallel lines can never have a common point. Hence it is an example of empty set.

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}.