Three friends, David, Emily, and Frank, were discussing the number of candies in a jar. David claimed, "There are at least $10$ candies." Emily stated, "There are at most $8$ candies." Frank then asserted, "Actually, there are at most $7$ candies." It turned out that all three statements were false. Let $c$ be the number of candies in the jar. Which of the following intervals is the set of all possible values of $c$?