Boolean Theorems - Simplify Function

I am currently taking a Discrete Mathematics course, along with Intro to Hardware course. I am having issues wrapping my head around Boolean Theorems, simplifying functions given to smaller circuit design. One problem that I am working on at the moment is:

F(a,b,c) = (A + C)(AB + AB`) + AC + C

I want to apologize for the formatting, but I did not see a shortcut in the toolbar above to format it correctly. I read through the theorems in the book, but I ended up finding my self more confused then I started with. I am looking for assistance in simplifying the function above, and also any help on tackling functions in the future.

I did construct a truth table to help determine how to simplify the function. From looking at the truth table, I did see that (A+C) & the function above have the same output. This conclusion seems as if (A+C) would be the simplified version of the original function, or at least be in the simplified version.

I know it is plain suicide taking both courses together, but somehow I have to overcome this hurdle. I appreciate any help provided.

Thank you,

~ KeiU

Here are some equalities that should get you to simplify your expression to $A+C$:

$AB+AB'=A$

$(A+B)(A+B')=A$

Absorption

$A+AB=A$

$A(A+B)=A$

• Hello, So, my truth table was right, that I should be working to simplify it towards (A +C)? I appreciate your answer, and working it out now. – Kei U. Jan 25 '17 at 12:33
• @KeiU. So were you able to get to $A + C$? – Bram28 Jan 25 '17 at 20:42
• Hello @Bram28, I was able to get it work and really appreciate your reply! – Kei U. Feb 1 '17 at 17:57