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24 votes
24 votes

The simplified SOP (Sum of Product) from the Boolean expression

$$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$$ is 

  1. $(\bar{P}.Q+\bar{R})$
  2. $(P+\bar{Q}.\bar{R})$
  3. $(\bar{P}.Q+R)$
  4. $(P.Q+R)$

7 Answers

Best answer
28 votes
28 votes
K-map
K-map

Answer is B

edited by
9 votes
9 votes
(P+Q'+R').(P+Q'+R).(P+Q+R')

=(P+R`)(Q+Q`)(P+Q`+R)

=P+PR+PQ`+R`P+R`Q`

=P(1+Q`)+R`P+R`Q`

=P(1+R`)+R`Q`

=P+R`Q`
edited by
2 votes
2 votes
Given Boolean Expression:

(P+Q'+R').(P+Q'+R).(P+Q+R')

we know that dual of a boolean expression is equivalent. Take dual of it:

PQ'R'+PQ'R+PQR'

Now simplify it.(I am taking dual because solving the given expression will be difficult hence, take dual and solve it)

=PQ'(R'+R)+PQR'

=PQ'+PQR'

=P(Q'+QR')

=P(Q'+R').

Now if we see option b) and take dual of it then we will be getting the above simplified expression.
Answer:

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