Question

Which one of the following is an example of a non-empty set?
A.Set of all even prime numbers
B.$\left\{ {x:{x^2} - 2 = 0{\text{ and }}x{\text{ is rational}}} \right\}$
C.\[\left\{ {x:x{\text{ is a natural number, }}x < 8{\text{ and simultaneously }}x > 12} \right\}\]
D.\[\left\{ {x:x{\text{ is a point common to any two parallel lines}}} \right\}\]

Answer 1

Hint: In the question, we are given four options and we have to find out which out of four is an example of a non-empty set. We will check the conditions and limits in all the four options and we will check which situation holds true according to the asked question which is to tell that which is an example of non-empty set.

Complete step-by-step answer:
In the given question we had asked to tell that which one out of four given options an example of non-empty set non-empty set is nothing but a set which contains one or more elements. We can also say that a non-empty set is other than an empty set.
Now, in the question, we are given four options and we have to tell which out of four an example of non-empty set is. So, we will pick the conditions one by one and then check that which an example of non-empty set is
In option (A), we are given that all even prime numbers are examples of non-empty sets or not even prime numbers are $2$ . Because $2$ is an even number as well as prime (Prime numbers are those which are divisible by only). Since $2$ is there, therefore the set of even prime numbers is non – empty and in option (B), the second set, $\sqrt 2 $ is a rational number. It means $\sqrt 2 $ cannot be there in the second set. Therefore the second set is empty.
In option (C), Again there is no natural number which is less than $8$ and greater than $12$ simultaneously, which means the third set is also empty.
In option (D),
It is impossible to have a common point between two parallel lines as parallel lines do not intersect. So the last set is also empty.
Therefore option (A) is the only set which is an example of non-empty set.

Note: Non-empty set is also known as non void set, where void means empty. If we take an example of empty set which is $A = \left\{ {x:9 < x < 10,x{\text{ is 0 natural numbers}}} \right\}$ will be a null set because there is no natural number between numbers 9 and 10. Empty set is denoted by $\left\{ {} \right\}{\text{ or }}\phi {\text{ but }}\left\{ \phi \right\}$ does not exist.