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?

Following questions are based on the information provided below:
$A \times B$ means $A$ is mother of $B$.
$A - B$ means $A$ is brother of $B$.
$A + B$ means $A$ is sister of $B$.
$A \div B$ means $A$ is father of $B$.
How is $K$ related to $M$ in $R \div M - K$?

Pointing to a photograph,Vipul said,"She is the daughter of my grandfather's only son." How is Vipul related to the girl in the photograph?

$A + B$ 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 $P = R + Q$ mean?

Rahul told Anand,'Yesterday $I$ defeated the only brother of the daughter of my grandmother.' Whom did Rahul defeat?

$A$ is the brother of $R$. $C$ is the mother of $B$. $M$ is the sister of $C$. How is $M$ related to $B$?