Perfect Induction and Counterexamples

# Perfect Induction and Counterexamples - Counterexample xyz...

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Mallard ECE 290: Computer Engineering I - Spring 2007 - Graded Web... https://mallard.cites.uiuc.edu/ECE290/webgrade.cgi?SessionID=mding3... 1 of 2 1/25/2007 10:52 PM Graded WebQuiz: Perfect Induction and Counterexamples You have submitted this WebQuiz 1 time (including this time). You may submit this WebQuiz a total of 10 times and receive full credit. Question #1 Use the truth table below to prove the following Boolean equation: (x + y') z = [ (x + y + z') (x' + y + z') (x' + y' + z') ] ' Note: LHS and RHS stand for "left-hand-side" and "right-hand-side", respectively. x y z x+y' LHS x+y+z' x'+y+z' x'+y'+z' (x+y+z')(x'+y+z')(x'+y'+z') RHS 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 You have filled in the truth table correctly. You received a raw score of 100% on this question. Question #2 Disprove the following by finding a counterexample: (x + y) (x + z') (x' + y) = y

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