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

(i) {x: x is a perfect square}

(ii) {x: x is perfect cube}

(iii) {x: x + 5 = 8}

(iv) {x: 2x + 5 = 9}

(v) {x: x ≥ 7}

(vi) {x: x ∈ N and 2x + 1 > 10}

Asked by Abhisek | 1 year ago |  74

1 Answer

Solution :-

(i) Given that,

The set of natural number is the universal set

To find the complement of the set of perfect squares.

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

 {x: x is a perfect square}´ = {x: x ∈ N and x is not a perfect square}

 

(ii) Given that,

The set of natural number is the universal set

To find the complement of the set of perfect cube

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

{x: x is a perfect cube}´  = {x: x ∈ N and x is not a perfect cube}

 

(iii) Given that,

The set of natural number is the universal set

To find the complement of {x: x + 5 = 8}

x +5 =8

x = 3

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

{x: x + 5 = 8}´ = {x: x ∈ N and x ≠ 3}

 

(iv) Given that,

The set of natural number is the universal set

To find the complement of the {x: 2x + 5 = 9}

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

2x +5 = 9

2x = 4

x = 2

{x: 2x + 5 = 9}´ = {x: x ∈ N and x ≠ 2}

 

(v) Given that,

The set of natural number is the universal set

To find the complement of {x: x ≥ 7}

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

{x: x ≥ 7}´ = {x: x ∈ N and x < 7}

 

(vi) Given that,

The set of natural number is the universal set

To find the complement of the {x: x ∈ N and 2x + 1 > 10}

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

2x +1>10

2x > 9

\( x>\dfrac{9}{2}\)

{x: x ∈ N and 2x + 1 > 10}´ = {x: x ∈ N and x ≤ \( \dfrac{9}{2}\)}

Answered by Sudhanshu | 1 year ago

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