42 a tautology is a statement that is always true, no matter what the truth values of its components use a truth table to show that false - p is a tautology for any statement p false p false → p false true true false false true 43 a refutation system is a logical system.
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47 translate the definition of the gcd in exercise 46 into prolog compare its efficiency to euclids’ gcd algorithm as given in figure 41 below is the code for the eculid’s gcd from the text on page 121.
A k-map is an alternate representation of a truth table in the form of a box 2 x 2 squares as shown the possible values of x (0,1) are used as labels for the rows and the possible values of y (0,1) are used as labels for the columns.