Question

$\mathbb{ \ \ Q\ U\ E\ S\ T\ I\ O\ N\: \: }$
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}



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Answer 1

1) A Null set is a set that doesn′t contain any element. Here, (i) Set of odd natural numbers divisible by 2: There can′ be any odd number that is divisible by 2.

2) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Now we have to write the set of even prime numbers from 1 to 50. Number 2 is the only prime even number.

3) Solution. {x: x is a natural number, x < 5 and x > 7} is a null set because a number cannot be simultaneously less than 5 and greater than 7.

4) Two parallel lines do not meet and as such have no common point. Hence, E is a null set. Collection of all odd integers. ... The collection is well defined and hence it forms a set.

Answer 2

(i) A set of odd natural numbers divisible by 2 is a null set because no odd number is

divisible by 2.

(ii) A set of even prime numbers is not a null set because 2 is an even prime number.

(iii) {x: x is a natural number, x < 5 and x > 7} is a null set because a number cannot

be simultaneously less than 5 and greater than 7.

(iv) {y: y is a point common to any two parallel lines} is a null set because parallel lines

do not intersect. Hence, they have no common point.