Question

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 1

(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.