$(20$ points$)$ Let $Y$ be the set of possible worlds. Recall that $F_{\text{:}}$is player $i\text{'}$s partition of $Y$ into disjoint information sets, and that for a given world $inY,F_i()$ is the information set in $F_7$ that contains $.$ Recall that given an event AsubeY, the set of all worlds where player i knows $A$ is defined as: $K_i(A)=\{inY$:$F_i()subeA\}.$ Prove the following statements. $($a$)(5$ points$)$ For any two events $A,$BsubeY,$K_i(A)K_i(B)=K_i(AB)$