Which of the following are examples of empty set?(i) Set of all even n

1.	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» (i) Since, all numbers ending with 0. Here, except 0 is divisible by 5 and are even natural number. Thus it is not an example of empty set. (ii) Since, 2 is a prime number and is even, and it is the only prime which is even. Therefore this not an example of the empty set. (iii) Here, x² – 2 = 0, x² = 2, x = ± √2 ∈ N. There is not natural number whose square is 2. Therefore it is an example of empty set. (iv) There is no natural number less than 8 and greater than 12. Thus it is an example of the empty set. (v) Here, no two parallel lines intersect at each other. Thus 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}.

Answer»

(i) Since, all numbers ending with 0. Here, except 0 is divisible by 5 and are even natural number. Thus it is not an example of empty set.

(ii) Since, 2 is a prime number and is even, and it is the only prime which is even. Therefore this not an example of the empty set.

(iii) Here, x² – 2 = 0, x² = 2, x = ± √2 ∈ N. There is not natural number whose square is 2. Therefore it is an example of empty set.

(iv) There is no natural number less than 8 and greater than 12. Thus it is an example of the empty set.

(v) Here, no two parallel lines intersect at each other. Thus it is an example of empty set.