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 }

Explanation

To find the complements of the given sets with respect to the universal set of natural numbers, we will follow a systematic approach. The complement of a set A, denoted as A', consists of all elements in the universal set that are not in A.

Let’s denote the universal set of natural numbers as \( U = \{1, 2, 3, 4, 5, \ldots\} \).

### Step-by-Step Solution

1. **Set (i):** \( A = \{ x : x \text{ is an even natural number} \} \)
- The complement \( A' \) will be the set of all natural numbers that are not even, which are the odd natural numbers.
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