Question

Which one of the following is an example of non-empty set?

• A. Set of all even prime numbers
• B. $\{x:x^2-2=0$ and $x$ is rational$\}$
• C. $\{x:x$ is a natural number, $x<8$ and simultaneously $x>12$$\}$
• D. $\{x:x$ is a point common to any two parallel lines$\}$

Answer 1

Answer: (A)

Set of all even prime numbers

• $2$ is the only even prime number .
• So the set of even prime numbers is non-empty.
• Since $\sqrt{2}$ is an irrational number, so the second set is empty.
• Again there is no natural number which is $<8$ and $>12$ simultaneously. So the third set is also empty.
• It is impossible to have a common point between two parallel lines as they don't intersect. So the last set is also empty.