I have a question that states the following:
Use algebraic manipulation to show that for three input variables x1 , x2 , and x3
∑(1,2,3,4,5,6,7) = x1 + x2 + x3
I'm assuming it wants the minimum sum of products to prove its equality to x1 + x2 + x3 (or x + y + z). This is what I've narrowed it down to so far: y'z + x'y + xz' + xyz.
However, I'm unable to understand which property's will reduce this to just x + y + z (or again, x1 + x2 + x3).
Best Answer
In the list of terms 1, 2, 3, 4, 5, 6, 7 only term 0 is missing. Term 0 corresponds to a conjunction of the three inverted variables. Therefore, you can look at the inverse function and invert it to get the desired function:
$F = (F')' = (x' y' z')'$
The first of De Morgan's law states:
This leads to:
$F = x + y + z$