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

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

(i) {xx is an even natural number}

(ii) {xx is an odd natural number}

(iii) {xx is a positive multiple of 3}

(iv) {xx is a prime number}

(v) {xx is a natural number divisible by 3 and 5}

(vi) {xx is a perfect square}

(vii) {xx is perfect cube}

(viii) {xx + 5 = 8}

(ix) {x: 2x + 5 = 9}

(x) {xx ≥ 7}

(xi) {xx ∈ N and 2x + 1 > 10}

Solution:

U = N: Set of natural numbers

(i) {xx is an even natural number}´ = {xx is an odd natural number}

(ii) {xx is an odd natural number}´ = {xx is an even natural number}

(iii) {xx is a positive multiple of 3}´ = {xx ∈ N and x is not a multiple of 3}

(iv) {xx is a prime number}´ ={xx is a positive composite number and x = 1}

(v) {xx is a natural number divisible by 3 and 5}´ = {xx is a natural number that is not divisible by 3 or 5}

(vi) {xx is a perfect square}´ = {xx ∈ N and is not a perfect square}

(vii) {xx is a perfect cube}´ = {xx ∈ N and is not a perfect cube}

(viii) {xx + 5 = 8}´ = {xx ∈ N and x ≠ 3}

(ix) {x: 2x + 5 = 9}´ = {xx ∈ N and x ≠ 2}

(x) {xx ≥ 7}´ = {xx ∈ N and x < 7}

(xi) {xx ∈ N and 2x + 1 > 10}´ = {xx ∈ N and ≤ 9/2}

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