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 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}.

Answer 1

(i) {x : x is an odd natural numbers} 

(ii) {x : x is an even natural numbers} 

(iii) {x: x is a natural number and not multiple of 3} 

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

(x) {x : x ∈ N and x is not divisible by 3 and 5} 

(xi) {x: x ∈ N and x is not a perfect square} 

(xii) {x:x ∈ N and x is not a perfect cube} 

(xiii) {x:x ∈ 2V and x ≠ 3} (ix) {x:x ∈ 2V and x ≠ 2} 

(x) {1,2,3,4,5,6} 

(xi) {x:x ∈ N and 2x + 1 ≤ 10} = {1, 2, 3, 4}.