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?


1 Answer 1


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

  • \$\begingroup\$ are you sure the first term was duplicated? Looks like an additional term was added. \$\endgroup\$ Apr 15, 2016 at 18:33
  • \$\begingroup\$ @TimSpriggs what do you suggest \$\endgroup\$
    – Coursal
    Apr 15, 2016 at 18:44
  • \$\begingroup\$ @Tim It does not change the result if you add same value again in OR combination. \$\endgroup\$
    – Darko
    Apr 15, 2016 at 18:51
  • 2
    \$\begingroup\$ @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 \$\endgroup\$ Apr 15, 2016 at 18:52
  • \$\begingroup\$ I guess I'm not as good at Boolean as you guys. And that's no Boole. \$\endgroup\$ Apr 15, 2016 at 19:33

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