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