Week 4 Homework

Week 4 Homework - 1. Use a t ruth table to determine...

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Unformatted text preview: 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 Y Z X' Z' (X' v Y) (X^(Y^Z))v[X' v ((X^Y)^Z'] 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 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. L.H.S. = [ (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 if we have four variables out of four variable then one mark in map If we have 3 variables out of four variable then 2 mark in map if we have 2 variables out of four variable then 2^2= 4 mark in map if we have only 1 variable out of four variable then 2^3= 8 mark in map ...
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Week 4 Homework - 1. Use a t ruth table to determine...

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