Question

Which of the following are the 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 lt 5 and x gt 7`}
(iv) {y : y is a point common to any two parallel lines}.

Answer 1

(i) Odd natural numbers are 1,3,5,7,9,11,…. None of these numbers is divisible by 2
`:.` Set of odd natural number divisible by 2
= empty set `= phi`
(ii) Collection of prime natural numbers
`= 2,3,5,11,13,..`
`rArr` Set of even prime natural numbers = {2}
Therefore, the set of even prime natural numbers is not an empty set
(iii) {x : x is a natural number `x lt 5 and x gt 7`} = a natural number which is smaller than 5 and greater than 7
`because` No such numbere is possible
Thus, {x : x is natural number, `x lt 5 and x gt 7`} is an empty set
(iv) {y : y is a point common to any two parallel lines}
`because` There is no common point in two parallel lines. therefore, {y : y is a point common to any two parallel lines} is an empty set.