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 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} 

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

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

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

(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} 

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

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

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

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

(x) {x: x ≥ 7}´ = {x: x N and x < 7} (xi) {x: x N and 2x + 1 > 10}´ = {x: x N and x ≤ 9/2}