Introducing a man to her husband,a woman said,"his brother's father is the only son of my grandfather." How is the woman related to this man?

$A + B$ means $A$ is the son of $B$; $A - B$ means $A$ is the wife of $B$; $A \times B$ means $A$ is the brother of $B$; $A \div B$ means $A$ is the mother of $B$; and $A = B$ means $A$ is the sister of $B$.
What does $P \times R + Q$ mean?

$A + B$ means $A$ is the father of $B$; $A - B$ means $A$ is the wife of $B$; $A \times B$ means $A$ is the brother of $B$; $A \div B$ means $A$ is the daughter of $B$. If $P + R + S + Q$,which of the following is true?

Pointing to a lady,Rajan said,"She is the daughter of the woman who is the mother of the husband of my mother." Who is the lady to Rajan?

Read the following information carefully and answer the question given below. All the six members of a family $A, B, C, D, E,$ and $F$ are travelling together. $B$ is the son of $C$ but $C$ is not the mother of $B$. $A$ and $C$ are a married couple. $E$ is the brother of $C$. $D$ is the daughter of $A$. $F$ is the brother of $B$. How is $E$ related to $D$?

$A$ family consists of six members $P, Q, R, X, Y,$ and $Z$. $Q$ is the son of $R$ but $R$ is not the mother of $Q$. $P$ and $R$ are a married couple. $Y$ is the brother of $R$. $X$ is the daughter of $P$. $Z$ is the brother of $P$. How is $Q$ related to $X$?