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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2015-05-26T22:06:37+05:30

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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 }

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