Having some problem with beginner boolean algebra. Somehow I can't figure out these two problems.
Show that LHS is equal to RHS:
$wx + w'y + xyz = wx + w'y.$ Can't find a way to "remove" $xyz$.
$zy' + yx' + z'x = z'y + y'x + zx'.$ Tried different theorems but can't go from LHS to RHS.
Would appreciate the help, been trying for 5 hours...
One of the ways to "remove" the summands is to use the absorption law $A + AB = A.$ Sometimes you need to add more variables to a summand by using the complementation law $A = xA + x'A.$
In the first problem, to remove $xyz$ using previous summands we need to add $w$ variable to it (since both of them contain it). We have the following chain of equalities: \begin{align}wx + w'y + xyz &= wx + w'y + wxyz + w'xyz \\ &= wx + (wx)(yz) + w'y + (w'y)(xz)\\ &= wx + w'y. \end{align}
For the second, add all variables (using complementation), regroup the summands and remove variables (again using complementation): \begin{align} zy' + yx' + z'x &= zy'x + zy'x' + yx'z + yx'z' + z'xy + z'xy'\\ &= z(y'x) + z'(y'x) + y(zx') + y'(zx') + x(z'y) + x'(z'y)\\ &= y'x + zx' + z'y. \end{align}