I have come across a couple questions while doing my digital logic work.
1) Is it possible to simplify these, while keeping each a product of sums? (I'm leaning towards no--the only way I could see to simplify them would be to distribute.) They're separate problems. $(a+b+c)(a'+b'+c')$ $(x+y)(x'+y+z')$
2) Find the minimum sum of products expression (I honestly didn't even know how to begin this one, if you could just get me started...): $x_1'x_3'x_5'+x_1'x_3'x_4'+x_1'x_4x_5+x_1x_2'x_3'x_5$ - The hint was to use the consensus theorem: $xy+yz+x'z=xy+x'z$
3) Find the minimum product of sums expression (again, if you could just help me get started) $x_1x_3'+x_1x_2+x_1'x_2'+x_2'x_3$
Any help is greatly appreciated! Thanks!