When do we consider a boolean expression "fully simplified"? (Eg, is $B'+ BA'C$ the simplest form of $AB'C + A'BC+ A'B'C+A'B'C'+AB'C'$?) Edit:
I have simplified a boolean expression (see below) and there still some terms who share the same element (it is very hard to simplify more). So,

When do we consider a boolean expression to be "fully simplified" (can't be simplified anymore)?

Here is an example:

$$AB'C + A'BC+ A'B'C+A'B'C'+AB'C'$$
where ($'$) means "not". For this example, I think the expression can not be simplified more than this: $$B'+ BA'C$$

So, is there any way to make sure the expression can't be simplified any more?
Thanks in advance
 A: In this case there is a further simplification you can make, viz to $B + A'C$.
In general, the problem of finding the simplest of the expressions that are equivalent to a given boolean expression is a hard one. 3-SAT is NP-complete, and that is only a subset of the general problem. In 3-SAT, the expression is the "and" of some terms, each of which is the "or" (or $+$ in your notation) of three variables, any of which might be negated. Something like this: $$(A+B+C)(A'+C'+D)(C+D'+E)$$ Then the task is to find whether or not the given expression is "satisfiable" or not. "The expression is not satisfiable" is equivalent to "The expression is equivalent to False". If the expression is not equivalent to False, 3-SAT does not ask for the simplest equivalent expression. So the general problem of finding the simplest equivalent expression is at least as hard as 3-SAT.
A: Here is a Vietch Diagram supporting the logic of reduction to   $\quad\textbf{B'+A'C}$

Note how I labeled the (A,A), (B,B'), (C,C') cells outside the big rectangle so they overlap. The result you seek comes from taking the largest rectangular area(s) found after entering the data.
Note the rectangle for terms $(5,1,3,4)\implies B')\quad$ and $\quad (2,3)\implies A'C$.
I did this in EXCEL, entering, for example $\quad 1(AB'C)\quad$ because it let me keep track of which terms had been entered, and verify they afterward. Note, If $A'C$ had been in the original terms, you would have had  to enter it in the cells currently occupied by $2$ and $3$. You'll have to develop your own means of keeping track of stuff. This just works for me and I'm $70$.  I hope this helps explain the usage of Vietch diagrams.
