What Is the Output of F = A + B.C in Boolean Algebra?

[jackson6612]

I'm new to this math world, so please explain your reply in as much detail as possible. Thank you.

Please have a look on this link (Example 6.4):
http://img84.imageshack.us/img84/3667/img0023hg.jpg

Boolean function is $$F=A+\overset{\_\_}{B}.C$$. I don't understand even the first step. I don't understand what it means by saying that the function has three variables A, B, and C. The first term A is missing two variables (B and C).

Please help me. Thank you for your time.

 

[mathman]

The first step is simply saying any set (A) can br expressed as the intersection of itself and the whole space. Furthermore the union of any set (B) and its complement (B') = the whole space. Putting this together and you get A=A.(B + B')=A.B + A.B'

. means intersection, + means union.

 

[jackson6612]

Thank you, Mathman.

But these things 'intersection' and 'uniion' are studied under topics of sets. That Boolean function is part of Boolean algebra involving logic gates. So, could you please deal it that way? Further, I don't even get what the question is asking. Could you please shine a light on this too? Thank you very much for all the guidance and your time.

 

[mathman]

The algebra of "logic gates" and the algebra of sets are essentially identical. I happen to be used to sets, so I express it that way. union is equivalent to "or", intersection is equivalent to "and" and complement is equivalent to "not".

As for

The first term A is missing two variables (B and C).

, all the author is saying you can always throw in [B or (not B)] without changing anything.