Question

Which of the following sets are empty?

• A. $A=\left\{\text{Prime numbers between 19 and 23}\right\}$
• B. $B=\{x:x\text{is an odd integer divisible by 2}\}$
• C. $C=\{x:-10<x<2,x\text{is a natural number}\}$
• D. $D=\{x:x\text{is an even prime number greater than 2}\}$

Answer 1

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

The correct options are
A $A=\left\{\text{Prime numbers between 19 and 23}\right\}$
B $B=\{x:x\text{is an odd integer divisible by 2}\}$
D $D=\{x:x\text{is an even prime number greater than 2}\}$

Consider $A=\left\{\text{Prime numbers between 19 and 23}\right\}$.
There are no prime numbers between 19 and 23.
Thus, $A=\left\{\right\}$, an empty set.
Let $B=\{x:x\text{is an odd integer divisible by 2}\}$. No odd integer is divisible by 2, and thus, $B=\left\{\right\}$, an empty set.
If $C=\{x:-10<x<2,x\text{is a natural number}\}$, then $C=\left\{1\right\}$ as 1 is the only natural number between -10 and 2. Thus, $C$ is a singleton set (and not an empty set).
Let $D=\{x:x\text{is an even prime number greater than 2}\}$. 2 is the only even prime. There are no even primes greater than 2 as any even number greater than 2 is divisible by 2, and hence not a prime. Thus, $D=\left\{\right\}$, an empty set.