Question

Which of the following sets are “empty sets”?

• A. $A$ = {set of prime numbers, less than $2$}
• B. $B=\left\{x\right|x+8=x\mathrm{and}\mathrm{x}\in \mathrm{N}\}$
• C. $C=\left\{0\right\}$
• D. $D=\left\{x\right|x$ is a point common to any two parallel lines$\}$

Answer 1

Answer: (A), (B), (D)

$D=\left\{x\right|x$ is a point common to any two parallel lines$\}$

$A=${set of prime numbers, less than $2$}

There is no prime number less than $2$. Hence, set $A$ is an empty set.

$B=\left\{x\right|x+8=x\mathrm{and}\mathrm{x}\in \mathrm{N}\}$

When we solve $x+8=x$, we get, $8=0$, which is a false statement. Hence set $B$ is an empty set.

$C=\left\{0\right\}$

Set $C$ contain an element, i.e. $0$; it is a singleton set.

$D=\left\{x\right|x$ is a point common to any two parallel lines$\}$

Parallel lines are the lines which never meet and the distance between them remains constant. So, it is not possible that they have a common point. Therefore, set $D$ is an empty set.

Hence, $A,B,D$ are empty sets.