Which laws simplify this boolean expression?

Question

Which laws do I need to use to simplify

!X + (!Y + !Z)*(Y + Z)

to

!X + (Y*!Z) + (!Y*Z)

Answer 1

You can first start by distributivity of multiplication over addition:

!X + (!Y + !Z)*(Y + Z) = !X + !Y*Y + !Z*Y + !Y*Z + !Z*Z

Then, we can use complementation to remove elements of the form !p*p:

= !X + 0 + !Z*Y + !Y*Z + 0

And finally remove the 0 as they are +'s neutral.