Answer to Question #173533 in Discrete Mathematics for ANJU JAYACHANDRAN

Question

5. a) Write the expression x1 ∨x2 ∧x3 ∨x4 in conjunction normal form and disjunctive

normal form

Answer 1

Let's write the expression in conjunctive normal form:

${x_1} \vee {x_2} \wedge {x_3} \vee {x_4} = {x_1} \vee {x_4} \vee {x_2} \wedge {x_3} = \left( {{x_1} \vee {x_2} \vee {x_4}} \right) \wedge \left( {{x_1} \vee {x_3} \vee {x_4}} \right)$

${x_1},\,{x_2} \wedge {x_3},\,\,{x_4}\,$ are elementary conjunctions, so the expression is already written in disjunctive normal form: ${x_1} \vee {x_2} \wedge {x_3} \vee {x_4} = {x_1} \vee \left( {{x_2} \wedge {x_3}} \right) \vee {x_4}$

Answer: CNF: $\left( {{x_1} \vee {x_2} \vee {x_4}} \right) \wedge \left( {{x_1} \vee {x_3} \vee {x_4}} \right)$ , DNF: ${x_1} \vee \left( {{x_2} \wedge {x_3}} \right) \vee {x_4}$