Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {x: x is an even natural number}

(ii) {x: x is an odd natural number}

(iii) {x: x is a positive multiple of 3}

(iv) {x: x is a prime number}

(v) {x: x is a natural number divisible by 3 and 5}

Asked by Abhisek | 11 months ago |  71

1 Answer

Solution :-

(i) Given that,

The set of natural number is the universal set

To find the complement of the set of even natural number

The complement of set A is the set of all elements of U which are not the elements of A.

{x: x is an even natural number}´ = {x: x is an odd natural number}

 

(ii) Given that,

The set of natural number is the universal set

To find the complement of the set of odd natural number

The complement of set A is the set of all elements of U which are not the elements of A.

{x: x is an odd natural number}´ = {x: x is an even natural number}

 

(iii) Given that,

The set of natural number is the universal set

To find the complement of the set of positive multiples of 3

The complement of set A is the set of all elements of U which are not the elements of A.

 {x: x is a positive multiple of 3}´ = {x: x ∈ N and x is not a multiple of 3}

 

(iv) Given that,

The set of natural number is the universal set

To find the complement of the set of prime number

The complement of set A is the set of all elements of U which are not the elements of A.

{x: x is a prime number}´ ={x: x is a positive composite number and x = 1}

 

(v) Given that,

The set of natural number is the universal set

To find the complement of the set of natural number divisible by 3 and 5

The complement of set A is the set of all elements of U which are not the elements of A.

 {x: x is a natural number divisible by 3 and 5}´ = {x: x is a natural number that is not divisible by 3 or 5}

Answered by Pragya Singh | 11 months ago

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