Question

Consider three sets
X
=
{
5
,
6
}
,
Y
=
{
2
,
3
,
4
}
and
Z
=
{
n
|
n
∈
N
,
n
is a prime number less than
10
}
. Consider the universal set to be
U
=
{
x
|
x
∈
N
,
x
<
15
}
. Which of the following options are correct?

Answer 1

Answer:

Step-by-step explanation:

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

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}