midterm2f07 - CS 2603 - APPLIED LOGIC FOR HARDWARE AND...

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CS 2603 — A PPLIED L OGIC FOR H ARDWARE AND S OFTWARE 11/19/07 Midterm Examination 2 Fall 2007 1 Assume that f and g are predicates that both have the same universe, non-empty universe of discourse. Use the inference rules of natural deduction (not the equations of Boolean algebra) to prove the following theorem. (∃ x .( y .( f ( x ) g ( y )))) |– (( x . f (x)) ( x . g ( x ))) 2 Assume that f and g are predicates that both have the same universe of discourse. Use the Boolean equations of predicate calculus to prove that the following equation is true. (( x .( f ( x ) g ( x ))) ( x . g ( x ))) = ( x . g ( x )) 3 Prove the following proposition. n .P( n ), where P( n ) ( length ( zipWith z [ x 1 , x 2 , . .. x n ] [ y 1 , y 2 , . .. y n ]) = n ) 4 Suppose that the following equations are true f[x] = [ ] {f 1} f(x 1 : (x 2 : xs)) = x 1 : (f(x 2 : xs)) {f 2} Prove the following proposition. n
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This test prep was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.

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