Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets $${S_1}$$ and $${S_2}$$ in C, either $${S_1}\, \subset \,{S_2}$$ or $${S_2}\, \subset \,{S_1}$$. What is the maximum cardinality of C?

A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is:

An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the tails are independent, the expected number of tosses are