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

Question

enter image description here

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

Answer 1

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.