Which are the following examples of the null set, give reason

(i) Set of even numbers divisible by 3.

(ii) {x : x is a common point to any two parallel lines}

(iii) Set of odd numbers divisible by 2.

(iv) {x : x is a natural number, x < 4 and x > 6}

(v) Set of even prime numbers.

Answers:

(i) Set of even numbers divisible by 3 is a null set, because no even number is divisible by 3.

(ii) {x : x is a common point to any two parallel lines} is a null set, because parallel lines do not intersect each other, so they have no common point.

(iii) Set of odd numbers divisible by 2 is a null set, because no odd number is divisible by 2.

(iv) {x : x is a natural number, x < 4 and x > 6}, is a null set,

natural numbers x > 4 = 1, 2, 3, and

natural numbers x > 6 = 7, 8, 9, 10….

because there is no any number simultaneously that is less than 4 and greater than 6. So it is a null set.

(v) Set of even prime numbers, is not a null set, because

set of even prime numbers = 2, 3, 5, 7, 11, 13, 17,…. and

2 is an even prime number, so it is not a null set.