Taking the set of natural numbers as the universal set, write down the

1.	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» (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}.

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»

(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}.