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**juliie** Use the laws of Boolean algebra to show that the identity (xy V x'y')' = x'y V xy' holds. Give all necessary steps and state explicitly which laws you are using. You may use de Morgan’s laws without deriving them yourself. I have no idea of how to even start or which of the laws to use. Please help!!!

Hi juliie!

The 2nd De Morgan law states: $\displaystyle (a \vee b)' = a' \wedge b'$.

Now let $\displaystyle a = xy$ and $\displaystyle b=x'y'$.

Then

$\displaystyle (xy \vee x'y')' = (a \vee b)' = a' \wedge b'$

Now back substitute those expressions for a and b:

$\displaystyle a' \wedge b' = (xy)' \wedge (x'y')'$

This is the first step.

Can you apply the 1st law of the De Morgan on (xy)' and also on (x'y')'?