Option A is saying that "For all possible Pairs $(x,y)$, $x$ and $y$ are same and have passed chemistry and physics exam." .. It would Only be True when there is Only One element(Student) in the Domain and He has passed in both Chemistry and Physics.
Option B says that "For All Pairs $(x,y)$, If $x$ has passed Physics and $Y$ has passed Chemistry then $x = y$." Or you use the Contrapositive that "For All Pairs $(x,y)$, If $x \neq y$ then either $x$ has not passed Physics Or $y$ has not passed Chemistry".
None of the Options is Correct for the Statement "There is Exactly One person who has Passed Both Exams"