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Boolean algebra problem

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JillsWarden

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I having trouble with the equation A+AB=A. I understand the logic, it's the rephrasing that bothers me. A+(A*B)=A still makes perfect sense. A(1+B) is where I get lost. It makes sense the answer is
A, I don't understand how they get to that equation. It goes from OR-AND to AND-OR. Any help will
be appreciated. I have to make sense of it in my head not just take it as a rule.
 

A+AB=A

A*1 + A*B = A
A * (1+B) = A
A * (1) = A

See this page: **broken link removed** search for the Distribution section.
 

After you have understood that, try to prove this : A+BC = (A+B)*(A+C)
 

I must look like an idiot but I still don't understand how 1 replaces A and becomes ORed with B. I'm obsessive and my mind won't let this go. I still don't see

A + AB = A
A + A*B = A still ok here.
you show
A*1 + A*B = A and I'm lost.
where does the 1 come from and not have to be
A*1 + A*B = A*1 with regular algebra. Then how do you get
A(1+B) and how does 1 replace A. I've looked at several sites and it's the same equation I just can't see
it and it's driving me crazy. The logic makes perfect sense just not that part of the equation.
 

I'm not the most articulate person. My question is simply how you get this
A + AB = A to
A*1 + A*B = A to
A(1 + B)
 

I really appreciate your patience with me on this, it finally clicked. I don't know why I couldn't get the equation to make
sense but understood the logic of it. Thank you for your help.
 

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