= Solution
The capacity of a <discrete memoryless channel> is $C=\max_{P_X}I(X;Y)$, in bits per channel use. For the <binary symmetric channel> with crossover probability $p$, $H(Y\mid X)=h(p)$ and $H(Y)\le1$. A uniform input makes the output uniform, attaining
$$
\boxed{C_M=1-h(p)}.
$$
For the <binary erasure channel>, let $E$ be its erasure indicator. This flag is visible in the output and <independent> of the input. If there is no erasure, the output reveals the input; otherwise it reveals nothing. Consequently
$$
I(X;Y)=(1-\epsilon)H(X),\qquad\boxed{C_N=1-\epsilon},
$$
again attained by a uniform input. These formulas include crossover probabilities zero and one, and complete erasure.
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