Which of the following are examples of the null set. (i) Set of odd n

1.	Which of the following are examples of the null set. (i) Set of odd natural numbers divisible by 2. (ii) Set of even prime numbers. (iii) {x : x is a natural numbers, x < 5 and x >7} (iv) { y: y is a point common to any two parallel lines}.
Answer» (i) There is no odd natural number divisible by 2. Therefore, given set is an empty set / nullset. (ii) 2 is the even prime number. ∴ Given set = {2} ≠φ (iii) There is no natural number x, which is simultaneously less than 5 and greater than 7. So, given set is null set. (iv) We know that two parallel lines have no common point and hence the given set is null set.

Which of the following are examples of the null set. (i) Set of odd natural numbers divisible by 2. (ii) Set of even prime numbers. (iii) {x : x is a natural numbers, x < 5 and x >7} (iv) { y: y is a point common to any two parallel lines}.

Answer»

(i) There is no odd natural number divisible by 2. Therefore, given set is an empty set / nullset.

(ii) 2 is the even prime number.

∴ Given set = {2} ≠φ

(iii) There is no natural number x, which is simultaneously less than 5 and greater than 7. So, given set is null set.

(iv) We know that two parallel lines have no common point and hence the given set is null set.