Question

Write the complement of {x:x belong to N and x is divisible by 3 and 5}.

Answer 1

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∈Nandx<7}

(xi) {x:xϵNand2x+1>10}

′

={x:x∈Nandx≤

2

9

}