Taking the set of natural numbers as the universal set,{x: x is a perfect square}

(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 ≤ \( \dfrac{9}{2}\)}