Deterministic and randomized communication complexity of set equality
For the first point, try a counting argument. How many different messages $m(a)$ can $B$ receive, if $|m(a)|&lt;n$? How many different strings can $A$ have?

For the second point, try first analyzing the trivial randomized protocol (randomly fixing $\log(n)$ positions of the string and sending these bits of $a$). Clearly, this protocol always accepts if $a=b$. Assume $a\neq b$, what is the probability that $\log(n)$ randomly picked bits are the same? Does that suffice?