Abstract Algebra Theory and Applications - Computer Science ...

EXERCISES 311Table 17.1. Boolean polynomialsx y x ′ x ∨ y x ∧ y0 0 1 0 00 1 1 1 01 0 0 1 01 1 0 1 1Programming ExercisesA Boolean or switching function on n variables is a map f : {O, I} n →{0, I}. A Boolean polynomial is a special type of Boolean function: it is anytype of Boolean expression formed from a finite combination of variables x 1 , . . . , x ntogether with O and I, using the operations ∨, ∧, and ′ . The values of the functionsare defined in Table 17.1. Write a program to evaluate Boolean polynomials.References and Suggested Readings[1] Donnellan, T. Lattice Theory. Pergamon Press, Oxford, 1968.[2] Halmos, P. R. “The Basic Concepts of Algebraic Logic,” American MathematicalMonthly 53 (1956), 363–87.[3] Hohn, F. “Some Mathematical Aspects of Switching,” American MathematicalMonthly 62 (1955), 75–90.[4] Hohn, F. Applied Boolean Algebra. 2nd ed. Macmillan, New York, 1966.[5] Lidl, R. and Pilz, G. Applied Abstract Algebra. Springer-Verlag, New York,1984.[6] Whitesitt, J. Boolean Algebra and Its Applications. Addison-Wesley, Reading,MA, 1961.