Question

Which of the following are examples of empty set?
(i) Set of all even natural numbers divisible by $5$
(ii) Set of all even prime numbers.
(iii) $\{x:x^2-2=0$ and $x$ is rational $\}$
(iv) $\{x:x$ is a natural number, $x<8$ and simultaneously $x>12$
(v) $\{x:x$ is a point common to any two parallel lines $\}$

Answer 1

Answer

Empty set is a set which does not contains any element.

i] Set of all even natural numbers divisible by 5

$\to$ Not a Empty set, e.q. 10, seven natural number &

divisible by 5.

ii] Set of all even prime number

$\to$ not a Empty set e.q. 2 is even prime number

iii] $\{x:x^2-2=0$ & x is rational $\}$

$\to$ not a Empty set, e.q. x=2 satisfy which is a

rational number.

iv] $\{x:x$ is a natural number x < 8 & x > 12 $\}$

$\to$ It is a empty set because if a natural number is less

than 8, then it cannot be greater than 12.

v] $\{x:x$ is a point common to any two parallel lines $\}$

$\to$ A empty set because there will be no common

point between two parallel lins.

So (iv) & (v) are examples of empty of empty sets.