Question 34 of 47intermediate🔧 ApplyShort Answer4 marks

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}

Answer

{x : x is an odd natural number}

(ii)

{x : x is an odd natural number}

Answer

{x : x is an even natural number}

(iii)

{x : x is a positive multiple of 3}

Answer

{x : x ∈ N and x is not a multiple of 3}

(iv)

{x : x is a prime number}

Answer

{x : x ∈ N and x is not a prime number}

(v)

{x : x is a natural number divisible by 3 and 5}

Answer

{x : x ∈ N and x is not divisible by 15}

(vi)

{x : x is a perfect square}

Answer

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

(vii)

{x : x is a perfect cube}

Answer

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

(viii)

{x : x + 5 = 8}

Answer

{x : x ∈ N and x ≠\neq 3}

(ix)

{x : 2x + 5 = 9}

Answer

{x : x ∈ N and x ≠\neq 2}

(x)

{x : x ≥\geq 7}

Answer

{x : x ∈ N and x < 7}

(xi)

{x : x ∈ N and 2x + 1 > 10}

Answer

{x : x ∈ N and x < 5}

Explanation

This question tests understanding of complement of a set. As per Definition 7 in the textbook, the complement of A is the set of all elements of U which are not elements of A. Symbolically, A' = {x : x ∈ U and x ∉ A}. Here, U is the set of natural numbers N = {1, 2, 3, 4, ...}. For each part, we identify elements in the given set and then write the complement as those natural numbers NOT in that set.

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