Blood Relations

Question

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

A) X is the mother-in-law of R.

B) P and R are not married to each other.

C) P is the son of X and Y.

D) Q can not be married to R.

I got answer as C ,but given is D. My approach :- As P,Q are children of X,Y. And if P is the son then X must be grandfather of S.But as Grandfather of S is Z,so P must be daughter.Please correct my approach if wrong

Answer 1

This is the picture I get:

Assuming $W$ and $Z$ are not just different labels for the same couple that is $X$ and $Y$, the only way for $Z$ to be the grandfather of $S$ who is the daughter of $P$ is for $P$ to be married to a child of $W$ and $Z$. This could be $R$, but does not have to be, so I labelled that person $?$.

The only ones whose gender we know for sure are Z and S, but assuming that couples are heterosexual, you can also conclude W is female.

From this, we see that:

A) X is the mother-in-law of R.

Not necessarily, since we don't know the gender of $X$, and this also depends on $R$ being the mystery person $?$. So this could be true, and could be false.

B) P and R are not married to each other.

If $R$ and the mystery person $?$ are one and the same, then $P$ and $R$ are married to each other. But if $R$ and $?$ are different, then they are not married to each other. So this could be true or false.

C) P is the son of X and Y.

Maybe, maybe not. We don't know the gender of $P$

D) Q can not be married to R.

If $R$ and $?$ are the same, then $Q$ cannot be married to $R$, but if $R$ and $?$ are different, then $Q$ can be married to $R$. So this could be true or false.

So .... I don't know what to tell you. It looks like all four claims could be either true or false.

Now, if you assume $R$ is the mystery person $?$, then $A$ can still be true or false, $B$ would have to be false, $C$ can be true or false, and $D$ would be true. So then it would be $B$

If you assume $R$ and $?$ are different people, then $A$ is false, $B$ is true, $C$ we don't know, and $D$ is false (it is false that $Q$ cannot be married to $R$, since $Q$ can be married to $R$)

Answer 2

Answer should be $B$.

As $P$ is parent of $S$ , and $X,Y$ are parent of $P$ , so either of $X,Y$ should have been the grandfather , but grand father is $Z$, which means $P$ is married to their child, $R$.

Hence $B $ is false