Answer

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**Hint:**We have to check all the conditions from I to IV whether they are true or not by using the given data. We take some examples of the numbers and check the validation for each equation to get the required answer.

**Complete step by step answer:**

It is given that $a,b,c$ are prime numbers, $x$ is an even number, and $y$ is an odd number.

We have to solve that one by one,

The first condition $a + x = b$ is true.

We can prove it by giving an example like $3 + 4 = 7$ , where $a = 3$, is a prime number and $x = 4$ is an even number and $b = 7$ is also a prime number.

The second condition $b + y = c$ is true.

It can also be proved by an example like $2 + 1 = 3$, where $b = 2$ is a prime number and $y = 1$ is an odd number and $c = 3$ is also a prime number.

The third condition $ab = c$ is not true.

This can be proved by an example like $5 \times 3 = 15$, where $a = 5$ and $b = 3$ both are prime numbers but $c = 15$ is not a prime number.

The fourth condition is $a + b = c$ also true.

It is also proved by an example like $2 + 3 = 5$ where $2, 3, 5$ are prime numbers.

Hence all the parts are satisfied with the given data.

Finally, we get the third condition only never true.

**Thus the correct option is C.**

**Note:**

Prime numbers are those numbers that are only divisible by itself or $1$. For example $2, 3, $ etc.

Odd numbers are those numbers that can never be divided by $2$. For example $9, 15$ etc.

Even numbers are those numbers which are always divisible by $2$and have no remainder. For example $6, 8$ etc.

It is to be kept in mind that when a prime number is multiplied by a prime number, it can never be a prime number.

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