simplification of F=A'B'C'+A'B'C+ABC'

Question

have i grouped them right? is the answer A'B'+C' or not???

The top-left circle containing two 1's is correct, but notice the circle across the corner contains no don't care. Otherwise you're correct. — poyea, Jun 03 '18 at 13:05
can you be more specific? shouldnt have i circled the top left with the bot right??? — Rafael, Jun 03 '18 at 13:19
Please edit your previous question by clicking the "edit" button to add more context instead of asking the exact same question. — user061703, Jun 03 '18 at 13:36

score 0 · Answer 1 · answered Jun 03 '18 at 15:25

No, you can't group together two diagonal cells; the cells you group must always be adjacent to each other ... touching in a corner is not enough.

Indeed, here is a counterexample to your proposed equivalence:

$A = 0, B=1, C=0$

Then $A'B'C'+A'B'C+ABC'=0+0+0=0$

but $A'B'+C'=0+1=1$

And another counterexample is:

$A = 1, B=0, C=0$

For then $A'B'C'+A'B'C+ABC'=0+0+0=0$

but $A'B'+C'=0+1=1$

How did I find those counterexamples? Because these are the top right and bottom left corners that you mistakenly grouped into $C'$ when putting together the top left and bottom right corner.

simplification of F=A'B'C'+A'B'C+ABC'

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