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I need to solve this in boolean algebra:

$$B(A+(B'+ A)')$$

Here is my attempt:

$$B(A+(B'+ A)')=B(A+(BA'))=B((AA')+(AB))=B(0+AB)=B(AB),$$

and the result should be just $B$. Should I just decide what is the right result (because I see it depents on $B$) or can I somehow adjust the result so it would end up just with $B$?

Random Jack
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trolkura
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1 Answers1

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There is a mistake in your chain of transformations. You're transforming $B(A+BA')$ into non-equivalent expression $B(AA'+ AB)$. So there is no way to adjust your result to end up with $B$.

One way to obtain $B$ using equivalent transformations is the following $$B(A+(B'+A)') = B(A+A'B) = BA + BA'B = AB + A'B = (A+A')B = 1B = B.$$

Here we are using the following identities: $$ A'' = A,\ (A+B)' = A'B',\ AA = A,$$ $$A(B+C) = AB + AC,\ AB = BA,\ A + A' = 1.$$

Random Jack
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