A problem in mathematics is given to three students $A, B$, and $C$, whose chances of solving it independently are $\frac{1}{2}, \frac{1}{3}$, and $\frac{1}{4}$ respectively. Find the probability that the problem is solved.

Two problems in mathematics are given to two students $A$ and $B$. The probabilities that $A$ and $B$ solve a problem independently are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. Find the probability that: (a) The problem is solved. (b) Exactly one of them solves the problem. (c) Neither solves the problem.