EECS 2001 Quiz: EECS2001 quiz1-S15

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Make sure your test has 3 pages, including this cover page. Answer in the space provided. (if you need more space, use the reverse side of the page and indicate clearly which part of your work should be marked. ) Let a = {n n : 1 n2 10} and b = {ab, d}. Give an explicit listing of the all elements of the following sets. (a) a b = (b) a b = (c) the power set of b = Let l = {s {0, 1} : s does not contain 110 as a substring}. Draw the transition diagram for a (deterministic) nite automaton for the language l. you do not have to prove your answer is correct. Claim: for all k 0, the number of a"s in sk is (c) give a careful proof of the claim in part (b).

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