I am doing some mathematics, and I am currently stuck on something. I do not understand this part at all, how can one approach this?
No variable is used here.
Problem:
Simplify the following Boolean expressions as far as possible, using and stating which Boolean laws and axioms you use at every step.
$$(x+xy)'y'+x'$$
I simply have no idea how to approach this, and what is the best way to remember the steps in terms of approaching this problem and simplifying as far as possible.
- $(x+xy)'y'+x'$
- $(x' \cdot (xy)')y'+x'$ (First deMorgan law)
- $(x' + (x' + y'))y'+x'$ (Second deMorgan law)
- $(x'x' + x'y')y'+x'$ (Distributive law)
EDIT: This is how far I am getting, and I am still somehow overwhelmed and confused.
There are surely many ways to simplify the expression $$(x + xy)'y' + x'.$$ One is to use the absorption law $x + xy = x$ twice (along with commutativity, i suppose) to arrive at $$(x + xy)'y' + x' = x'.$$ If you have not yet proven this law in your course, you can do so by using more elementary laws, say by an argument like $$x + xy = x \cdot 1 + x \cdot y = x(1 + y) = x \cdot 1 = x,$$ or by making a truth table.