Examples of Empty Set
Examples of Empty Set
| Set |
Empty Set or Not |
Reason |
|
(i) Set of all even natural numbers divisible by 5
|
Not an Empty Set
|
Numbers like
\[
10,20,30,\ldots
\]
satisfy the condition.
|
|
(ii) Set of all even prime numbers
|
Not an Empty Set
|
\[
2
\]
is an even prime number.
|
|
(iii)
\[
\{x:x^2-2=0 \text{ and } x \text{ is rational}\}
\]
|
Empty Set
|
\[
x=\pm\sqrt2
\]
which are irrational numbers.
|
|
(iv)
\[
\{x:x \text{ is a natural number},\ x<8 \text{ and } x>12\}
\]
|
Empty Set
|
No natural number can satisfy both conditions simultaneously.
|
|
(v)
\[
\{x:x \text{ is a point common to any two parallel lines}\}
\]
|
Empty Set
|
Parallel lines never intersect.
|
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