The Gateway to Computer Science Excellence
+21 votes

If $P, Q, R$ are Boolean variables, then

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

  1. $P.\bar{Q}$

  2. $P.\bar{R}$

  3. $P.\bar{Q} + R$

  4. $P.\bar{R} + Q$

in Digital Logic by Veteran (52.1k points) | 2.4k views
If we take out p common from second bracket, function will be 0 when p=0

Take cases of p=1

Now when p=1 and because of third bracket when Q =1 function will be 0.

Hence we are left only with two min terms (P,Q,R) = 100 + 101.

Try doing such examples using truth table in exam won't take much time and increases accuracy.

2 Answers

+29 votes
Best answer
Ans is (A) $ P \bar Q $

$ (P + \bar Q)(P \bar Q + PR)(\bar P \bar R + \bar Q) $

$= (PP \bar Q + PPR + P \bar Q + P \bar QR)(\bar P \bar R + \bar Q) $

$= (P \bar Q + PR +  P \bar Q + P \bar QR)(\bar P \bar R + \bar Q) $

$= P \bar Q + P \bar QR $

$= P \bar Q $
by Loyal (5.9k points)
edited by
Sir how you get PQ'R'  in third step?
For those who don't like POS form to do simplification
Take complement->simplify in sop->take complement again to get the answer.

How to solve this using k-map?

Mistake in third step
Fixed now
Thanks a lot sir.
+5 votes


=( p'(q')' )'.{( (pr)'.(pq')' )'.( (p'r')'(q')' )'}

={(p'q)'.( (pr)'.(pq') )'} + (p'r')'q )'

=( p'q+(pr)'.(pq')' + (p'r')'q )'

=( p'q+ (p'+r')(p'+q)+(p+r)q )'

=(p'q +p'+ p'r'+qp'+qr'+pq+qr)'

=( p'(q+1) +p'r+ q(p'+p)+q(r'+r) )'





by (75 points)
simple method

assume p= q=r=1 calculate function value

check for same given option

some options will automatically eliminate .if same put another value
can you please elaborate it
take p=q=r=1

funcion will be 0

now put this p,q,r into given options c and d will not satisfy (eliminate )

for option a and b re evaluate the function by p=1 q= 0 r=1  function value= 1

put these into option a and b

it will eliminate b
No it will not eliminate @set2018 there will be conflict btw option (a) and (b)
1,1,0 can eliminate the conflict b/w a and b

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,650 questions
56,242 answers
95,940 users