CS208 Week 4 Homework

CS208 Week 4 Homework - CS208 Week 4 Homework November 8...

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Unformatted text preview: CS208 - Week 4 Homework November 8, 2010 Discrete Math CS 208 Online 1. Use a t ruth table to determine whether the Boolean expressions ( X^(Y^Z)) v [ X' v((X^Y)^Z'] and X' v Y a re equivalent. X 0 0 0 0 1 1 1 1 Y 0 0 1 1 0 0 1 1 Z 0 1 0 1 0 1 0 1 X' 1 1 1 1 0 0 0 0 Z' 1 0 1 0 1 0 1 0 (X' v Y) 1 1 1 1 0 0 1 1 (X^(Y^Z))v[X' v ((X^Y)^Z'] 1 1 1 1 0 0 1 1 Equivalent 2. Use theorem 10.1 to establish the validity of the equivalence in expression: [ (X v Y) ^ (X' v Y)] ^ [(X v Y') ^ (X' v Y')] = 0. S tart with the expression on t he left side. = [(X v Y) ^ (X' v Y)] ^ [(X v Y') ^ (X' v Y')] = [(X v Y) ^ (X' v Y)] = [(Y v X) ^ (Y v X')] ----------------------Theorem 10.1 (a) = Y v (X ^ X') ---------------------------------------------------------Theorem 10.1 (c) = (X ^ X') = 0 ---------------------------------------------------------Theorem 10.1 (f) & [(X v Y') ^ (X' v Y')] = [(Y' v X) ^ (Y' v X')]----------------------Theorem 10.1 (a) = Y' v (X ^ X') --------------------------------------------------------Theorem 10.1 (c) = (X ^ X') = 0 ---------------------------------------------------------Theorem 10.1 (f) = (Y v 0) = Y ; (Y' v 0) = Y'------------------------------------------Theorem 10.1 (g) therefore; Y ^ Y' = 0--------------------------------------------------------------Theorem 10.1 (f) Therefore, [(X v Y) ^ (X' v Y)] ^ [(X v Y') ^ (X' v Y')] = 0 3. Use the Karnaugh Map method to simplify the expression: (W ^ X' ^ Y ^ Z) v (W' ^ X' ^ Y ^ Z) v (W' ^ X ^ Y) v (Y' ^ Z) v (Y' ^ Z') ...
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This note was uploaded on 09/28/2011 for the course CS 208 taught by Professor Green during the Spring '08 term at Park.

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CS208 Week 4 Homework - CS208 Week 4 Homework November 8...

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