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) ${x : 2 x + 5 = 9}$
(x) ${x : x \geq 7}$
(xi) ${x : x ϵ N an d 2 x + 1 > 10}$

Question

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 : 2 x + 5 = 9}

(x)

{x : x \geq 7}

(xi)

{x : x ϵ N an d 2 x + 1 > 10}

Filo · Accepted Answer

U= N: Set of natural numbers(i) {x:xis an even natural number}′={x:x is an odd natural number}(ii) {x:xis an odd natural number}′={x:xis an even natural number}(iii) {x:x is a positive multiple of 3}′={x:x∈N and x is not a multiple of 3}(iv) {x:xis a prime number}′={x:xis a positive composite number and x=1}(v) {x:xis a natural number divisible by 3 and 5}′={x:xis a natural number that is not divisible by 3 or 5}(vi) {x:xis a perfect square}′={x:x∈Nand x is not a perfect square}(vii) {x:xis a perfect cube}′={x:x∈Nand x is not a perfect cube}(viii) {x:x+5=8}′={x:x∈Nand x=3}(ix) {x:2x+5=9}′={x:x∈Nandx=2}(x) {x:x≥7}′={x:x∈Nandx10}′={x:x∈Nandx≤29​}

Question Text	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) ${x : 2 x + 5 = 9}$ (x) ${x : x \geq 7}$ (xi) ${x : x ϵ N an d 2 x + 1 > 10}$
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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