[7 minutes] Using the various book and lecture Boolean identities, laws and expressions, minimize xy'+z+(x+y)z, to its lowest terms. When creating the function, use for not (ie. b), use xor for exclusive-or (ie. axorb), use xnor for exclusive-nor (ie.

Answer 1

b=(a'+b)(a+b')
Using DeMorgan's Law, we can simplify the expression xy' + z + (x + y)z as follows:

xy' + z + (x + y)z
= (xy' + z) + (x + y)z
= (xy' + z) + (xz + yz)
= xy' + z + xz + yz

Now, we can apply the distributive law to eliminate the parentheses:

xy' + z + xz + yz
= xy' + xz + yz + z
= x(y' + z) + (y + z)

Using the absorption law, we can further simplify:

x(y' + z) + (y + z)
= x + (y + z)
= x + y + z

So, the expression has been minimized to x + y + z.