Question

The set of even Prime numbers. Is it a finite, infinite or empty set?

Answer 1

Hint: First we see what are empty sets, infinite sets and finite sets. Then we will find the set of prime numbers. Using the set of prime numbers we will find the set of even prime numbers that is the set of those elements which are divisible by 2. At Last, we will see that the set of even prime numbers is empty sets, infinite sets or finite sets.

Complete step by step solution:
We should know the definition of empty, infinite and finite sets. So, that we find solution easily
If a set does not have any element or the cardinality of any set is zero then the set is empty.
If a set has a finite number of elements or countable elements the set is finite.
If a set has an infinite number of elements or uncountable elements the set is infinite.
Let S be the set of prime numbers
$S = \{ 2,3,5,7,11.......\} $
Let E be the set of even Prime numbers
$E = \{ 2\} $
Clearly, we can see that the cardinality of set E is one which is countable
Therefore, the set of even prime numbers is countable.

Note: Students might have a concept that a gaggle that's claimed to possess only one half is claimed to be Associate in Nursing empty set. they will have a concept that the cardinality of the set is up to at least one. Then we tend to be able to say that the set of even prime numbers is the Associate in Nursing empty set. However, we tend to all apprehend that the set of prime numbers is not an Associate in Nursing empty set. So, this thought got to be avoided. So, students have to bear in mind that a gaggle that's claimed to possess only one half is claimed to be a singleton set.