The question is A'B'C' + B'CD' + ABD + A'BCD + AB'C'D'. Also shown in this image which has the $2$ approaches I was going for.
When entering it on this site, it failed to simplify further, as shown in this image
What is the reason that if you go for option $2$ you won't be able to get the final answer? Or is there a way to get the final answer but the site can't figure it out? Or are there some rules which prevent me from going to option $2$? Or am I wrong entirely?
Well the website, is the problem, other websites simplify option 2 back to option 1
Try this website, paste this:
(A'*B'*C')+B*D*(A+C)+B'*D'*(A+C),so to your question:Yes, there is!
The steps to convert option 2 to 1:
$$ A'B'C'+BD(A+C)+B'D'(A+C)=A'B'C'+ABD+CBD+AB'D'+CB'D'$$$$ =(A'B'C'+AB'D'+CB'D')+ABD+CBD$$$$ =B'(A'C'+AD'+CD')+ABD+CBD$$$$ =B'(A'C'+(AD'+CD'))+ABD+CBD$$$$ =B'(A'C'+D'(A+C))+ABD+CBD$$$$ =B'(D'(A+C)+A'C')+ABD+CBD$$$$ =B'(D'(A'C')'+A'C')+ABD+CBD ...[a+b=(a'b')']$$$$ =B'(D'+A'C')+ABD+CBD ...[*]$$$$ =B'D'+A'B'C'+ABD+CBD $$$$ =B'D'+ABD+CBD+A'B'C' $$
hence proved!
[ * ] It's the redundancy law, identity b "$A+A'B=A+B$", where $A=A'C',B=D'$, in that step.
This is what the site should have not probably figured out, because the photo below says that the identity is not so popular!