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$\begin{align}

& \text{a) 4} \\

& \text{b) 5} \\

& \text{c) 1} \\

& \text{d) 2} \\

\end{align}$

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Now we are given that set A = {x: x is an even prime number}.

Now first we will understand what this means. The set given to us is written in set builder form. Now A = {x: x is an even prime number} is read as A is a Set of all the elements x such that x is an even prime number.

So now we have the condition to build the set which consists of even prime numbers.

Now we know that even numbers are the numbers that are in multiple of 2.

Also the prime number is any number which is divisible by just itself and 1. i.e. there is no other divisor of that number. For example 13 is prime because there is no number which divides 13 other than 1 and 13.

Now we need to find all the even prime numbers

The first even number that we come across is 2 which is prime

After that we know all the numbers are multiples of 2. Which means they are divisible by 2 and hence those numbers will not be prime numbers.

Hence the only even prime number is 2

Therefore A = {2}