Exam20081008 - 8. (5 points) Evaluate the following: a) 1/2...

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Csci 2610, Fall 2008 Exam 2 2008.10.08 1 Name: _________________________________ Seat:_______________ Exam 2 has 10 questions worth a total of 75 points. Please make certain you have all 4 pages. You will have 50 minutes to complete the exam. 1. (5 points) Given sets A = {1, 2, 3, 4} and B = {3, 4, 5, 6} find the following: a) A B b) A B c) A - B 2. (5 points) P(S) = { , {x}, {y}, {x, y}, {{x, y}}, {x, {x, y}}, {y, {x, y}}, S} is the power set of S. What is S? 3. (5 points) What is the sum of products expansion of F(x,y,z) = xy + z ? 4. (5 points) Prove the Absorption Law, x(x + y) = x, using only Boolean identities. You may not use the law itself in either of its forms.
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Csci 2610, Fall 2008 Exam 2 2008.10.08 2 5. (5 points) a) What is functional completeness as it relates to Boolean functions? b) Give an example of a functionally complete set. 6. (10 points) Construct a Boolean circuit for the XOR function, x y. 7. (10 points) Show f(x) = x 4 + 3x 2 + 4x + 7 is O(x 4 ) by finding witnesses to the relationship.
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Unformatted text preview: 8. (5 points) Evaluate the following: a) 1/2 b) -3.7 c) 8 d) -1/2 e) 3/2 + 1/3 Csci 2610, Fall 2008 Exam 2 2008.10.08 3 9. (15 points) A B, the symmetric difference of A and B, contains all elements in either A or B, but not in both A and B. Use a semantic proof to show that A B = (A B) (B A). Csci 2610, Fall 2008 Exam 2 2008.10.08 4 10. (10 points) A palindrome is a sequence that reads the same forward and backward. Examples include MOM, TOOT, ABLE WAS I ERE I SAW ELBA, and NOW, SIR, A WAR IS NEVER EVENSIR, A WAR IS WON! (Sometimes we make allowances for punctuation and spaces.) Write an algorithm hat accepts a list of n characters and returns 1 if the list is a palindrome and 0 otherwise. Your algorithm only needs to find simple palindromes, like the first three above. Dont worry about palindromes that require the elimination of punctuation and the shuffling of spaces....
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Exam20081008 - 8. (5 points) Evaluate the following: a) 1/2...

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