Boolean algebra help.

[DLMUK]

Hi,

I have a question in my HND to prove two Boolean expressions are the same using truth tables.

https://www.dropbox.com/s/45tbto58foezrdu/bool11.jpg?dl=0

I can see that the two parts of the expressions including variables ABC are the same. But the AC and BC parts don't to me.

For example I thought that for ~(AC) the B term is irrelevant. Therefore in a truth table you would get two events when the term is true, i.e. when B is a 0 and when B is a 1. Because it is only interested in terms A and C.

Is this correct?

Thanks

 

[jacoffey85]

It's been a while since I've done truth tables and boolean algebra, but here's what I come up with:

Simplify the equation down, reducing the "bars". The long bar over the entire equation will invert all of the logic for each section and should work out to:

A(B)C + AC + (B)C --- I'm using ( ) to denote a bar or "not".

Since AC is common in the first two parts, then you can use the Redundancy Law and eliminate the AC. Same with (B)C in the first and last part. This leaves you with just A(B)C = A(B)C

I hope I explained that well enough, it's been a while since I've studied all of the laws of boolean algebra.

 

[L D[AR2P#0.0]]

Generate two truth tables, one for each expression and the truth tables will be identical. QED

 

[L D[AR2P#0.0]]

.. well more than two required...