midterm1f07 - CS 2603 - APPLIED LOGIC FOR HARDWARE AND...

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CS 2603 — A PPLIED L OGIC FOR H ARDWARE AND S OFTWARE 9/26/07 Midterm Examination 1 Fall 2007 1 Consider the following proposition. (((a b) (b c)) ( ¬ b)) a) How many rows would a truth table for the proposition have? c) Classify the proposition as satisfiable, tautology, or contradiction. 2 a) Diagram a digital circuit representing the proposition of problem 1. b) Rewrite the proposition of problem 1 in proof-checker notation. 3 a) Supply the missing details in this proof. Assume it cites inference rules only, not theorems. b) Draw a box around each discharged assumption. c) State the theorem that the proof confirms. Use natural deduction to prove the following theorems, citing inference rules or theorems stated in the form of inference rules on the cribsheet. 4a (b c) |- (a b) c 5( b c) a |- (a b) (a c) Prove the following equations using the laws and theorems of Boolean algebra stated on the
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