CS70_fa02_mt1_sol - CS 70 Fall 2003 P RINT your name:...

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CS 70 Discrete Mathematics for CS Fall 2003 Wagner MT1 Solutions PRINT your name: , (last) (first) SIGN your name: PRINT your username on cory.eecs : WRITE your section number (101 or 102): This exam is open-book, open-notes. No calculators are permitted. Do all your work on the pages of this examination. If you need more space, you may use the reverse side of the page, but try to use the reverse of the same page where the problem is stated. You have 80 minutes. There are 4 questions, worth 25 points each (100 points total). The questions are of varying difficulty, so avoid spending too long on any one question. Do not turn this page until the instructor tells you to do so. Problem 1 Problem 2 Problem 3 Problem 4 Total CS 70, Fall 2003, MT1 Solutions 1
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Circle TRUE or FALSE. You do not need to justify your answers on this problem. N denotes the set of natural numbers, { 0 , 1 , 2 ,... } . Z denotes the integers, { ..., - 2 , - 1 , 0 , 1 , 2 ,... } . (a) TRUE or False : If the implication P = Q is true, then its converse is guaranteed to be true, too. (b) True or FALSE: w Z . x Z . y Z . z Z . w + x = y + z . (c) True or FALSE: x N . p Z . p > 5 = x 2 1 ( mod p ) . (d) True or FALSE: p Z . p > 5 = ⇒ ∃ x N . x 2 1 ( mod p ) . (e) True or FALSE: If m is any natural number satisfying m 1 ( mod 2 ) , then the equation 2048 x 1 ( mod m ) is guaranteed to have a solution for x . CS 70, Fall 2003, MT1 Solutions
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This note was uploaded on 10/23/2010 for the course CS 70 taught by Professor Papadimitrou during the Spring '08 term at University of California, Berkeley.

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CS70_fa02_mt1_sol - CS 70 Fall 2003 P RINT your name:...

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