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Question

Which of the following is/are null sets?


  1. A = { x:x N, 2 < x < 10 }

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

  3. C = { x:x is a rational number, x2 - 3 = 0 }

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


Solution

The correct options are
B

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


C

C = { x:x is a rational number, x2 - 3 = 0 }


D

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


A = {3, 4, 5, 6, 7, 8, 9}
 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.
B is a null set.

C = { }
x2 - 3 = 0  x = ±3 which is not a rational number. It is an irrational number.
C is a null set.

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

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