Answer
a) Here the sets are increasing. A bit string of length not exceeding 1 is also a bit string of length not
exceeding 2, so Ai ~ Az. Similarly, Az ~ A3 ~ A4 ~ · · · ~ An. Therefore the union of the sets Ai, Az, ... ,
An is just An itself.
b) Since Ai is a subset of all the Ai 's, the intersection is Ai , the set of all nonempty bit strings of length
not exceeding 1, namely {O, 1}.
Work Step by Step
a) Here the sets are increasing. A bit string of length not exceeding 1 is also a bit string of length not
exceeding 2, so Ai ~ Az. Similarly, Az ~ A3 ~ A4 ~ · · · ~ An. Therefore the union of the sets Ai, Az, ... ,
An is just An itself.
b) Since Ai is a subset of all the Ai 's, the intersection is Ai , the set of all nonempty bit strings of length
not exceeding 1, namely {O, 1}.
