# Is it possible, in Boolean Algebra, to add arbitrarily a new term to both sides of an expression?

First of all, i'm sorry for my english. I'll try to do my best to explain myself.

I've been trying to look for it on the internet, but i'm not sure about the answer. I hope someone can help me here :)

My question is: Is it possible to add a new term to both sides of a boolean algebra expression?

For example:

A * B' = 0, then

A * B' + A = 0 + A, then

A * B' + A = A

I know that in that equation specifically DOES work, but i'm not sure if it's absolutely acceptable always.

Thank you!

-
Maybe you can have a look at section 5: faculty.etsu.edu/tarnoff/ntes2150/ch5_v02.pdf – Amzoti Nov 21 '12 at 22:44
Interestingly, people who apologize for their English tend to have quite a high proficiency in English :-) – joriki Nov 21 '12 at 22:44
It is an axiom of equality that if $t=s$ then $f(t)=f(s)$ for any function $f$ defined on $t$ (or on $s$). (In particular, if $t=A*B'$ and $f(r)=r+A$ for $r,A,B$ in a Boolean algebra. The point is that this is not directly about Boolean algebras, but much more general.) Is this what you are talking about? (I may have misunderstood.) – Andrés Caicedo Nov 21 '12 at 22:44
Thanks, Amzoti. I went over the titles, and i think i have all that covered. I've been checking my notes for a while now, but i can't convince myself about the question I asked. Thank you anyway! I'm not sure i understood you correctly Andres Caicedo, but i think that what you meant is that if I apply a function, in this particular case, a function that adds A to the value the function takes as a parameter, then i can apply the function on the other side of the = sign, and the equality will still hold. So, it is possible to do what i ask, then... Thank you very much!! – Federico Nov 21 '12 at 23:01

## 1 Answer

If $A=B$ then $A+C = B+C$, but it's not generally true in Boolean algebras that if $A+C=B+C$ then $A=B$.

-
That was my doubt! Thank you very much!! I really appreciate it! I was trying not to use it, because i wasn't sure. You just solved one big question :) – Federico Nov 21 '12 at 23:06