midterm1Solutions - Solutions EE20n Midterm 1 Problem 1(24...

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1 of 5 Solutions – EE20n Midterm 1 Problem 1 (24 points) Please indicate whether the following statements are true or false. You will receive 0 points for a wrong answer, 1.5 points for no answer, and 3 points for a correct answer. There will be no partial credit. (a) If and are sets with one element, then is a set with two elements. Answer: False (b) If then , where is the number of elements in the set , and is the powerset of . Answer: True (c) The statement “If then ” is logically equivalent to the statement “If not then not ”. Answer: False (d) If a feedback composition is well formed, then it must be true that all the component state machines in the composition have state-determined outputs. Answer: False (e) If a non-deterministic machine A simulates another non-deterministic machine B and B also simulates A, then A and B are bisimilar. Answer: False (f) where are two sets that are subsets of a universe set and contain the elements in but outside of respectively. Answer: False (g) If , then . Answer: True (h) Answer: False A B A B × A 1 = P A ( ) 2 = A A P A ( ) A A B A B A B ( ) c A c B c = A B , U A c B c , U A B , A B graph f ( ) f A A [ ] ( ) { } graph f ( ) f A B [ ] ( ) { } Naturals Reals [ ] Reals Reals [ ]
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2 of 5 Problem 2 (30 points) (a) Suppose we input the periodic sequence “0101010101...” into a
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