Question

prove
(A+B). (Ā+c) (B+C) = (A+B) (Ā+c)​

Answer 1

I hope we are in a Boolean Algebra.

LHS=(b+a)(b+c)(a’+c)=(b+ac)(a’+c)=ba’+bc+0+ac as aa’=0, (where a’ denotes the complement of a) =ac+ba’+bc=ac+b(a’+c)=0+ac+b(a’+c)=aa’+ac+b(a’+c)= a(a’+c)+b(a’+c)=(a+b)(a’+c)=RHS. We have used distributivity of + over . and of . over + as well as cc=c.