Q. 33.8( 55 Votes )

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}

Answer :

For all parts, given that
(i) Let A = {x : x is an even natural number}


We want to find complement of A , which is given by U - A


A’ = U - A


A’ = {x:x ϵ N} - {x : x is an even natural number}


A’ = {x : x is an odd natural number}


(ii) Let A = {x : x is an odd natural number}


A’ = U - A


A’ = {x:x ϵ N} - {x : x is an odd natural number}


A’ = {x : x is an even natural number}


(iii) Let A = {x : x is a positive multiple of 3}


A’ = U - A


A’ = {x:x ϵ N} - {x : x is a positive multiple of 3}


A’ = {x : x is not a positive multiple of 3}


(iv) Let A = {x : x is a prime number}


A’ = U - A


A’ = {x: x ϵ N} - {x : x is a prime number}


A’ = {x : x is not a prime number}


(v) Let A = {x : x is a natural number divisible by 3 and 5}


A = {x : x is a natural number divisible by 15}


A’ = U - A


A’ = {x: x ϵ N} - {x : x is a natural number divisible by 15}


A’ = {x : x is a natural number not divisible by 15}


(vi) Let A = {x : x is a perfect square}


A’ = U - A


A’ = {x: x ϵ N} - {x : x is a perfect square}


A’ = {x : x is not a perfect square}


(vii) Let A = {x : x is a perfect cube}


A’ = U - A


A’ = {x: x ϵ N} - {x : x is a perfect cube}


A’ = {x : x is not a perfect cube}


(viii) Let A = {x : x + 5 = 8}


A = {x : x = 3}


A’ = U - A


A’ = {x: x ϵ N} - {x : x = 3}


A’ = {x : x ϵ N and x ≠ 3}


(ix) Let A = {x : 2x + 5 = 9}


A = {x : x = 2}


A’ = U - A


A’ = {x: x ϵ N} - {x : x = 2}


A’ = {x : x ϵ N and x ≠ 2}


(x) Let A = {x : x ≥ 7}


A’ = U - A


A’ = {x: x ϵ N} - {x : x ≥ 7}


A’ = {x : x < 7}


(xi) Let A = {x: x ϵ N} - {x : 2x + 1 > 10}


A = {x: x ϵ N and x > 9/2}


A’ = U - A


A’ = {x:x ϵ N} - {x: x ϵ N and x > 9/2}


A’ = {x: x ϵ N and x < 9/2}


A’ = {1, 2, 3, 4}


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