How do I simplify Boolean simplification ABC + AB' . ( A' C') + A'BC?

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Homework Help Overview

The discussion revolves around simplifying a Boolean expression involving terms like ABC, AB', and A'BC. Participants are exploring the implications of multiplication in Boolean algebra and the simplification process.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to simplify the expression by examining the multiplication of terms, particularly AB' and (A' C'). There is confusion regarding the application of Boolean identities, such as AA' = 0, and how this affects the overall expression.

Discussion Status

Some participants have provided steps in the simplification process, noting that certain terms cancel out. There is an ongoing exploration of the implications of these cancellations, but no consensus has been reached on the final simplified form.

Contextual Notes

Participants are working under the constraints of Boolean algebra rules and are questioning the correctness of their simplifications and assumptions about the terms involved.

adnankhuram
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ABC + AB' . ( A' C') + A'BC

I am confused in AB' . ( A' C')

the multiplication would be AA'B'C' OR AA'C'+A'B'C'
 
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adnankhuram said:
ABC + AB' . ( A' C') + A'BC

I am confused in AB' . ( A' C')

the multiplication would be AA'B'C' OR AA'C'+A'B'C'

It is AA'B'C'.

ehild
 
Abc + ab' . ( a' c') + a'bc

abc + aa'b'c' + a'bc

abc + b'c' + a'bc ( aa' = 0)

bc(a + b'c' +a')

bc (a+a'+b'c') as a+a' = 1

bc( b'c')

bb'cc'

0

is this is right
 
adnankhuram said:
Abc + ab' . ( a' c') + a'bc

abc + aa'b'c' + a'bc

abc + b'c' + a'bc ( aa' = 0)

As aa'=0 the second term cancels. You have abc+a'bc. Continue from here.

ehild
 

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