J is the married man.
Note that a person's sister-in-law may be the wife of that person's brother or the sister of that person's spouse.
There are 2 cases:
1. If B's legal spouse is J, then J's sibling must be P and P's sister-in-law must be B.
2. If B's legal spouse is P, then P's sister-in-law must be J and J's sibling must be B.
It is given that B's legal spouse and J's sibling are of the same sex. Also, it is obvious that P's sister-in-law is female. Then, B's legal spouse and J's sibling both must be males.
B's spouse J's sibling P's sister-in-law
(male) (male) (female)
------------------------------------------------------
Case I J P B
Case II P B J
Case II is not possible as B & P are married to each other and both are male. Hence, J is the married man.
