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# H4 - CS123 Youssef Homework 4 Due Date Problem 1(25 points...

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CS123 March 30, 2010 Youssef Homework 4 Due Date: April 20, 2010 Problem 1: (25 points) Let ( B, + , , 0 , 0 , 1) be a Boolean algebra. Deﬁne the following operations and ± : x y = xy 0 + x 0 y , and x y = ( x + y ) 0 . a) Prove that x y = ( x + y )( x 0 + y 0 ) b) Evaluate x x , x 1, x 0, x 1, and x 0, all in terms of x , 0, 1, and ’. c) Express xy using the operation but without using +, , , or 0 . d) Express x + y using the operation but without using +, , , or 0 . Problem 2: (20 points) a) Suppose that there is a panel of 3 judges for some game, and that after each player completes his/her presentation, each judge enters his/her vote of yes or no (yes=1, no=0) into a machine. The machine tallies the votes, and returns 1 (that is, ”pass”) if at least two judges vote yes. Otherwise, the machine returns 0 (for ”fail”). Express the working of the machine as a Boolean function of three variables (the 3 judges’ votes).

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H4 - CS123 Youssef Homework 4 Due Date Problem 1(25 points...

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