UGC NET CSE | June 2016 | Part 2 | Question: 9

Question

The simplified form of the Boolean equation $(A\bar{B}+A\bar{B}+AC)(\bar{A}\bar{C}+\bar{B})$ is

• A. $A\bar{B}$
• B. $A\bar{B}C$
• C. $\bar{A}B$
• D. $ABC$

Comments

the simplified form of a Boolean equation (A' B + AB'C + AC) ( A' C' +  B') is :

 (1) A'B

(2) A'BC

(3) A'B

(4) ABC

Please Answer this Question . Because the question is this in the Net july2016 paper. all you are taking wrong question.

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IS THIS QUESTION RIGHT? WHY BECAUSE MY ANSWER IS NOT MATCHING WITH GIVEN OPTIONS..

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QUESTION :----    (AB'+AB'C+AC)(A'C'+B')

= (AB'(1+C)+AC)(A'C'+B')                              ((1+X)=1 SO (1+C)=1)

=(AB'+AC)(A'C'+B')

= AA'B'C'+AB'B'+ACA'C'+AB'C                       (x.x'=0   so A.A'=0 SO AA'B'C'=0,  AA'CC'=0))

=0+AB'B'+0+AB'C                                           (  x.x=x   so   B'.B'=B')

=AB'+AB'C

=AB'(1+C)

=AB'

SO OPTION 1 IS TRUE

Answer 1

A.AB'

(AB'+AB'+AC)(A'C+B')

(AB'+AC)(A'C'+B')

AB'A'C'+AB'B'+ACA'C'+ACB'

AB'B'+ACB' =AB'(C+1)=AB'

Answer 2

A option ans 

Answer 3

(AB` + AB`C + AC) (A`C` + B`)
= AB` +AB`C +AB`C
= AB` +AB`C
= AB`(1 + C)
= AB`
So, option (A) is correct.