Four members are given:

Mr. Horton, Mr. Horton’s wife, Mr. Horton’s son, Mr. Horton’s Mother

Given condition a) If the doctor is younger than the lawyer, then the doctor and the lawyer are not blood relatives.

So to fulfill this condition the doctor must be Mr. Horton’s wife and lawyer must be Mr. Horton because Husband-wife are not blood relatives but it contradicts condition b) i.e. If the doctor is a woman, then the doctor and the lawyer are blood relatives.

Thus it is clear that doctor is not younger than lawyer

Given condition c) If the lawyer is a man, then the doctor is a man.

⇒ Either Mr. Horton or his son is either doctor or lawyer.

And from condition a) we conclude that Mr. Horton is doctor and his son is a lawyer because otherwise condition a) is not possible.

From (1) and (3), T can not be the only daughter and have a sister (R or S). Hence, T is T’s brother i.e. D is a Male.

From (3), let’s say that R is T’s sister i.e. R is Female.

From (2), Q is S’s only son i.e. Q is Male.

But T is Q’s brother which means that Q is not S’s only son. Hence, our assumption was wrong. Thus, S is T’s sister i.e. S is Female. And R must be S’s only son. Now it is clear that T & R are Males and S is Female. Q must be a Male as only one of them is of opposite sex from each of the other three. And he is S & T’s brother.