Pointing to a woman,Nirmal said,"She is the daughter of my wife's grandfather's only child". How is the woman related to Nirmal?

$A + B$ 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 $P \times R - Q$,which of the following is true?

Pointing to a gentleman,Deepak said,"His only brother is the father of my daughter's father." How is the gentleman related to Deepak?

These questions are based on the following information. Study it carefully and answer the questions.
$(i)$ $A \times B$ means $A$ is father of $B$.
$(ii)$ $A \div B$ means $A$ is daughter of $B$.
$(iii)$ $A + B$ means $A$ is sister of $B$.
$(iv)$ $A - B$ means $A$ is husband of $B$.
Which of the following indicates $N$ is mother of $K$?

$A$ and $B$ are brothers,$C$ and $D$ are sisters. $A$'s son is $D$'s brother. How is $B$ related to $C$?

$A + B$ 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?