Module 04 Written Assignment 1. Write Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) corresponding to the following truth table: p T T T T F F F F q T T F F T T F F r Truth Value T T F T T F F F T F F T T T F F p q 2. Write DNF and CNF for the following formula: Also diagram a combinatorial (logic) circuit corresponding to this formula. p q 3. Write DNF and CNF for the following formula: Also diagram a combinatorial (logic) circuit corresponding to this formula. 4. Write DNF and CNF for the following formula: ( p q) ( p r) 5. Let U be the set of all math problems, that is, assume that all the x ' s below represent math problems. Define 4 predicates over U as follows: P ( x )=x is solvable Q ( x )=x is easy R ( x ) =x is hard Given the above, translate the following formulas into English: Problems Answers Module 04 Written Assignment (a) x (Q ( x) R ( x ) ) (b) x ( P ( x ) R (x )) (c) x ( P ( x ) Q ( x ) ) Given the above, translate the following English statements into quantified formulas: (d) Some hard problems are not solvable. (e) For all problems, if it is easy then it is solvable. 6. Find formulas in negation normal form equivalent to the following quantified formulas: (a) x ( P ( x ) Q ( x ) ) (b) x ( P ( x ) Q ( x ))