# Q. 3 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}

Universal set = U = {1,2,3,4,5,6,7....................}

(i) {x : x is an even natural number} = {2,4,6,8,..........}

{x : x is an even natural number}'= U - {x : x is an even natural number}  = {1,3,5,7,9,..........} = {x : x is an odd natural number}

(ii) { x : x is an odd natural number }' = U - { x : x is an odd natural number } = {x : x is an even natural number}

(iii)  {x : x is a positive multiple of 3}' = U -  {x : x is a positive multiple of 3} =  {x : x , x  N and is not a positive multiple of 3}

(iv) { x : x is a prime number }' = U - { x : x is a prime number } = { x : x is a positive composite number and 1 }

(v) {x : x is a natural number divisible by 3 and 5}' = U - {x : x is a natural number divisible by 3 and 5} = {x : x is a natural number not divisible by 3 or 5}

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