Question

Check whether 2 is the example of the null set of all even prime numbers.

Answer 1

Hint: A null set means that there are no values which satisfy the condition. A null set is called an empty set as well. Using the definition of null set and prime number we can solve this problem.

Complete step-by-step answer:
All even numbers (i.e.>2) are divisible by 2.
For example $\left( {4,6,8,10,............} \right)$ is the set of all even numbers greater than 2, and all these numbers are divisible by 2.
Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
But 2 is also an even number.
But it is divisible by 1 and 2 only.
i.e. 2 is a prime number.
$\Rightarrow$2 is a number which is both even as well as prime.
So, this is not an example of a null set or empty set.

Note: An empty set or null set means that there are no values which satisfy the condition, and So, first find out the set of all even prime numbers which has only one number which is 2, and 2 is not an example of a null set, according to the above condition.