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}
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Answer 1

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(i) Set of odd natural numbers divisible by 2 is a null set as odd numbers are not divisible by 2.

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

(iii) {x: x is a natural number, x < 5 and x > 7} is a null set as a number cannot be both less than 5 and greater than 7.

(iv) {y: y is a point common to any two parallel lines} is a null set as the parallel lines do not intersect. Therefore, they have no common point.

Answer 2

Answer:

Except (ii), every set is a null set.

Step-by-step explanation:

Odd numbers are divisible by 2 if 1 is subtracted.

2 is divisible by 2, and a prime number.

There can be no numbers which are smaller than 5 and greater than 7.

Any two parallel lines contain no common points.