A and Y is true means A.Y is true. It can only be possible when A is true and Y is true. So
1. A
2. A --> (X v Y v ~P)
From 1 and 2 By using modus ponen we have this.
3. (X v Y v ~P)
Now,
4. Y
5. B --> ~Y
From 4 and 5 by using modus tollen we have this.
6. ~B.
So A is true and B is false. Hence A.B is false. So option C should be correct.
For option D we already know that Y is true. Hence (X v Y) is also true. So option D is also correct.