NCERT Class XI Mathematics - Sets - Solutions
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Question : 7
Total: 73
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 number, x < 5 and x > 7}
(iv) {y : y is a point common to any two parallel lines}
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x : x is a natural number, x < 5 and x > 7}
(iv) {y : y is a point common to any two parallel lines}
Solution:
(i) Set of odd natural numbers divisible by 2 is a null set because odd natural numbers are not divisible by 2.
(ii) Set of even prime numbers is {2} which is not a null set.
(iii) {x : x is a natural number, x < 5 and x >7} is a null set because there is no natural number which satisfies x < 5 and x > 7 simultaneously.
(iv) {y : y is a point common to any two parallel lines} is a null set because two parallel lines do not have any common point.
(ii) Set of even prime numbers is {2} which is not a null set.
(iii) {x : x is a natural number, x < 5 and x >7} is a null set because there is no natural number which satisfies x < 5 and x > 7 simultaneously.
(iv) {y : y is a point common to any two parallel lines} is a null set because two parallel lines do not have any common point.
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