I guess some triggering information should be given in the question.
Considering level triggered circuit, insignificant processing delay at gates, and only one transition per gate per second.
I got a).
I wasn't sure that whether we are allowed to use the values of $X$ and $Y$ before the $1$st second (starting point of observation), so I put a don't care for $A$ there.
So value of A,B at timing 1,3,5,8 is A:-0,1,0,0 B:-1,0,1,1 So option A is right
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