Question

simplify to the minimum $(xy)+(x+y)z$
$(xy)+z$
$x+y+xyz$
$(xy)+xz+yz$
$(xy)+xyz$
there is no right answer

Explanation:

Step1: Apply De - Morgan's law on $(XY')'$ and $(X' + Y)'$

By De - Morgan's law, $(AB)'=A'+B'$ and $(A + B)'=A'B'$. So, $(XY')'=X'+Y$ and $(X' + Y)'=XY'$.

Step2: Substitute into the original expression

The original expression $[(XY')'+(X' + Y)'Z]$ becomes $(X'+Y)+XY'Z$.

Step3: Expand and simplify

We know that $A + BC=(A + B)(A + C)$. Here, we can rewrite it as $X'+Y+XY'Z$. Since $X'+XY'Z=X'(1 + Y'Z)+XY'Z=X'+X'Y'Z+XY'Z=X'+(X'+X)Y'Z=X'+Y'Z$. So the simplified expression is $X'+Y+XY'Z$.

Answer:

$X'+Y+XY'Z$