Question

Which of the following is/are null sets?

• A. A = { $x:x\in$ N, 2 < $x$ < 10 }
• B. B = { $x:x$ is an even prime number greater than 2 }
• C. C = { $x:x$ is a rational number, $x^2$ - 3 = 0 }
• D. D = {$x:x$ is an odd natural number divisible by 2}

Answer 1

Answer: (B), (C), (D)

The correct options are
B

B = { $x:x$ is an even prime number greater than 2 }

C

C = { $x:x$ is a rational number, $x^2$ - 3 = 0 }

D

D = {$x:x$ is an odd natural number divisible by 2}

A = {3, 4, 5, 6, 7, 8, 9}
$\therefore$ A is not a null set.

B = { }
2 is the only even prime number. There are no numbers greater than 2 that are even and prime.
$\therefore$ B is a null set.

C = { }
$x^2$ - 3 = 0 $\Rightarrow$ $x$ = ±$\sqrt{3}$ which is not a rational number. It is an irrational number.
$\therefore$ C is a null set.

D = { }
Odd numbers are not divisible by 2.
$\therefore$ D is a null set.