MAT299 Chapter Notes - Chapter 2: Atomic Formula, Propositional Calculus, Universal Quantification

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16 May 2020
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E. g. let p(x) be a function determining whether integer x is prime; p is predicate that forms an atomic formula when applied with integer x: variables could be free (not bound to specific domain of discourse) or bound. Let p(x) be summation of first x integers starting from 0 is equal to: existence quantifier ( ): means there exists an element in the domain x(x+1)/2; then x(p(x)) means the statement above holds for all integers. Let q(x) be 2n is greater than n! A b is not nnf, but its equivalent counterpart a b is in nnf form: disjunction normal form (dnf): nnf that comprises of ors of ands. E. g. (a c) (b c: conjunction normal form (cnf): nnf that comprises of ands of ors. A 2-value multiplexer (circuit in computer) has 3 inputs, two for data and one for control.

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