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}(vi) {x : x is a perfect square}(vii) {x : x is a perfect cube}(viii) {x : x + 5 = 8}(ix) {x : 2x + 5 = 9}(x) {x : x ≥ 7}(xi) {x : x ∈ N and 2x + 1 > 10}

For all parts, given that
(i) Let A = {x : x is an even natural number}

We want to find complement of A , which is given by U - A

A’ = U - A

A’ = {x:x ϵ N} - {x : x is an even natural number}

A’ = {x : x is an odd natural number}

(ii) Let A = {x : x is an odd natural number}

A’ = U - A

A’ = {x:x ϵ N} - {x : x is an odd natural number}

A’ = {x : x is an even natural number}

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

A’ = U - A

A’ = {x:x ϵ N} - {x : x is a positive multiple of 3}

A’ = {x : x is not a positive multiple of 3}

(iv) Let A = {x : x is a prime number}

A’ = U - A

A’ = {x: x ϵ N} - {x : x is a prime number}

A’ = {x : x is not a prime number}

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

A = {x : x is a natural number divisible by 15}

A’ = U - A

A’ = {x: x ϵ N} - {x : x is a natural number divisible by 15}

A’ = {x : x is a natural number not divisible by 15}

(vi) Let A = {x : x is a perfect square}

A’ = U - A

A’ = {x: x ϵ N} - {x : x is a perfect square}

A’ = {x : x is not a perfect square}

(vii) Let A = {x : x is a perfect cube}

A’ = U - A

A’ = {x: x ϵ N} - {x : x is a perfect cube}

A’ = {x : x is not a perfect cube}

(viii) Let A = {x : x + 5 = 8}

A = {x : x = 3}

A’ = U - A

A’ = {x: x ϵ N} - {x : x = 3}

A’ = {x : x ϵ N and x ≠ 3}

(ix) Let A = {x : 2x + 5 = 9}

A = {x : x = 2}

A’ = U - A

A’ = {x: x ϵ N} - {x : x = 2}

A’ = {x : x ϵ N and x ≠ 2}

(x) Let A = {x : x ≥ 7}

A’ = U - A

A’ = {x: x ϵ N} - {x : x ≥ 7}

A’ = {x : x < 7}

(xi) Let A = {x: x ϵ N} - {x : 2x + 1 > 10}

A = {x: x ϵ N and x > 9/2}

A’ = U - A

A’ = {x:x ϵ N} - {x: x ϵ N and x > 9/2}

A’ = {x: x ϵ N and x < 9/2}

A’ = {1, 2, 3, 4}

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