Computer Science
Show that dual of P'QR' + PQ'R + P'Q'R is equal to the complement of PQ'R + Q.(P'R' + PR')
Boolean Algebra
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Answer
Dual of P'QR' + PQ'R + P'Q'R:
(P'+Q+R').(P+Q'+R).(P'+Q'+R)
Complement of PQ'R + Q.(P'R' + PR'):
[PQ'R+Q.(P'R'+PR')]'
= (PQ'R)'.[Q.(P'R'+PR')]'
= (P'+Q+R').[P'QR'+PQR']'
= (P'+Q+R').(P+Q'+R).(P'+Q'+R)
Hence proved.
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