Question

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 perfect cube}
(viii)  {x: x + 5 = 8}
(ix)  {x: 2x + 5 = 9}
(x)  {x: \(x ≥ 7\)}
(xi)  {x: x \(\in\) N and \(2x + 1 > 10\)}

Answer 1

U = N: Set of natural numbers
(i) {x: x is an even natural number} ´ = {x: x is an odd natural number}

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

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(iii) {x: x is a positive multiple of 3} ´ = {x: x \(\in\) N and x are not a multiple of 3}

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

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(v) {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}

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(vi) {x: x is a perfect square} ´ = {x: x \(\in\) N and x is not a perfect square}

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(vii) {x: x is a perfect cube} ´ = {x: x \(\in\) N and x is not a perfect cube}

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(viii) {x: x + 5 = 8} ´ = {x: x \(\in\) N and x\(\neq\) 3}

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(ix) {x: 2x + 5 = 9} ´ = {x: x \(\in\) N and x \(\neq\) 2}

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(x) {x: x \(≥\) 7} ´ = {x: x \(\in\) N and x < 7}

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