# Using boolean simplification

Let's say we have this logic function:

g = abc + abc' + a'bc

and let's try to simplify this using laws

= ab(c+c') + a'bc

= ab + a'bc

and there's the point I stuck.

But using the good ol' Karnaugh map it seems that the result should be ab + bc

So, does absorption law apply here?

Or I got it all wrong from the start?

If you duplicate the first term:

g = abc + abc' + abc + a'bc

and reduce

g = ab(c+c') + (a+a')bc

you get

g = ab + bc

• are you sure the first term was duplicated? Looks like an additional term was added. Apr 15, 2016 at 18:33
• @TimSpriggs what do you suggest Apr 15, 2016 at 18:44
• @Tim It does not change the result if you add same value again in OR combination. Apr 15, 2016 at 18:51
• @TimSpriggs . using the identity that x = x+x (if x is true then x OR x is true, if x is false then x OR x is false). By the same reasoning then it holds that abc = abc + abc Apr 15, 2016 at 18:52
• I guess I'm not as good at Boolean as you guys. And that's no Boole. Apr 15, 2016 at 19:33