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) {xis a natural numbers, < 5 and > 7}

(iv) {yis a point common to any two parallel lines}

Asked by Pragya Singh | 2 years ago |  114

##### Solution :-

(i) Given that,

Set of odd natural numbers divisible by 2

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

There was no odd number that will be divisible by 2 and so this set is a null set.

The set of odd natural number divisible by 2 is a null set.

(ii) Given that,

Set of even prime numbers.

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

There was an even number 2 , will be the one and only even prime number. So the

set contains an element. So it is not a null set.

The set of even prime numbers is not a null set

(iii) Given that,

{x: x is a natural numbers, x < 5 and x > 7}

To find if the given statement is an example of null set A set which does not contain any element is called the empty set or the null set or the void set.

There was no number that will be less than 5 and greater than 7 simultaneously. So it is a null set

{x: x is a natural number, x < 5 and x > 7} is a null set

.

(iv) Given that,

{y: y is a point common to any two parallel lines}

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

The parallel lines do not intersect each other. So it does not have a common point of intersection. So it is a null set.

{y: y is a point common to any two parallel lines} is a null set

Answered by Abhisek | 2 years ago

### Related Questions

#### If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

#### Prove that A – B = A ∩ B.’

Prove that A – B = A ∩ B.’

#### Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.