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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 } NCERT Solutions for Class 11th Mathematics Chapter 1 Exercise 1.5 3

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U = set of natural numbers = N 1) { x : x is an odd natural number, x = 2 k +1, k ∈ N } 2) { x : x is an even natural number , x = 2k, k ∈ N } 3 ) {x : x = 3 k +1 or 3 k +2, k ∈ N } 4) {x : x is a composite number, x = p q, p and q ∈ N, and p ≠1, q ≠ 1 } 5) { x : x ≠ 15 k, k ∈ N } 6) { x : x ≠ k², k ∈ N } 7) { x : x ≠ k³ , k ∈ N } 8) { x : x ≠3 , x ∈ N - {3} } 9) { x : x ≠2 , x ∈ N - {2} } 10) { x : x < 7 } 11) { x : x <= 4.50 }