Introducing a man,a woman said,"He is the only son of my mother's mother." How is the woman related to the man?

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 $B$.
$D$ is brother of $B$. $M$ is brother of $B$. $K$ is father of $M$. $T$ is wife of $K$. How is $B$ related to $T$?

Given that:
$1.$ $A$ is the mother of $B$;
$2.$ $C$ is the son of $A$;
$3.$ $D$ is the brother of $E$;
$4.$ $E$ is the daughter of $B$.
The grandmother of $D$ is:

There are six persons $A, B, C, D, E$ and $F$. $C$ is the sister of $F$. $B$ is the brother of $E$'s husband. $D$ is the father of $A$ and grandfather of $F$. There are two fathers,three brothers,and a mother in the group. Who is the mother?

There is a family of six persons $A, B, C, D, E$ and $F$. They are Lawyer,Doctor,Teacher,Salesman,Engineer and Accountant. There are two married couples in the family. $D$,the Salesman,is married to the Lady Teacher. The Doctor is married to the Lawyer. $F$,the Accountant,is the son of $B$ and brother of $E$. $C$,the Lawyer,is the daughter-in-law of $A$. $E$ is the unmarried Engineer. $A$ is the grandmother of $F$. Which of the following is one of the couples?

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