Answer to Question #122790 in Discrete Mathematics for poojitha

Question

2. Obtain the product of sums canonical form of the following formula
i)(P^Q^R)V (¬P^Q^R)V(¬P^¬Q^¬R)

Answer 1

Truth table

P Q R F

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 0

1 1 0 0

1 1 1 1

Sum of product corresponding entry 1 of output column ,in the boolean function given in a truth table is

F=(P^Q^R) V(~p^Q^R)V(~P^~Q^~R)

Product of sum corresponding entry 0 of the output column ,boolean function given in truth table is

F=(P+Q+ ~R)(P+~Q+R)(~P+Q+R)

(~P+Q+~R)(~P+~Q+R)