M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statement is necessarily FALSE?

The correct answer is: W is the wife of P

To understand why this statement is necessarily FALSE, let us break down the information given in the question step-by-step:

1. Children and Marital Status:
M and N have four children: P, Q, R, and S.
Out of these four children, only P and R are married. Q and S are unmarried.

2. Offspring Association:
The problem states that they had children X and Y "respectively". This means:
P has child X.
R has child Y.

3. Parentage of Y:
We are told that Y is a legitimate child of W. Since we already know that R is the parent of Y, and Y is a legitimate child of W, it follows that R and W must be married to each other (i.e., W is the spouse of R).

4. Analyzing the Options:
Since W is married to R, W cannot be married to P (as P is a different sibling and is married to a different spouse, or W is already the spouse of R). Therefore, the statement "W is the wife of P" is contradictory and must be necessarily FALSE.