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

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