I have a homework question "Show the following is true using theorems. State which theorem you use at each step." This is just one of many problems I have! So, if you can help me with this one problem than I can apply what I learn to finish the rest. I don't want a handout; I just don't know where to start or what to do. I have looked through the different theorems in the book and I don't see how any would apply to this! Am i suppose to prove that the first part = the second?
$$A'BD' + BCD + ABC' + AB'D =\\ A'BD' + BCD + ABC' + AB'D + BC'D' + A'BC + ABD$$
Should I group two or more and work from there? Since, we are only working with '+' then I should only need these types of theorems?
I have a book that shows the different theorems. But it still doesn't help me tackle this problem. Are we to prove how the first part equals the second part? To me that's expanding and not reducing.
I can work either side i guess whichever is easier..
Here is a list of theorems the book provides $$\begin{align} & X + 0 = X&&\\ & X + 1 = 1&&\\ & X + X = X&&\\ & X + X' = 1&&\\ & X + Y = Y + X&&\\ & (X + Y) + Z = X +(Y + Z)&&\\ & X \times (X + Y) = X&&\\ & X \times Y + X \times Y' = X&& \end{align}$$
these are most of them. there are a few others.. The book i am using is digital logic - principles and practices.