# Thread: Sets-Using De Morgan's Law

1. ## Sets-Using De Morgan's Law

Can anyone run through the answer to this for me.
I'm a bit confused.

Let X and Y be subsets of some universal set U.
Use De Morgan's Laws to show that:
______
(X n Y ) n Y is equal to one of the following:

_
X n Y
_
X u Y

X

Y

2. Hello, mcdonagh521!

Let $\displaystyle X$ and $\displaystyle Y$ be subsets of some universal set $\displaystyle U.$

Use DeMorgan's Laws to show that: .$\displaystyle (\overline{X \cap Y}) \cap Y$ is equal to one of the following:

. . $\displaystyle (a)\;\overline X \cap Y \qquad(b)\;\overline X \cup Y \qquad(c)\;X \qquad (d)\;Y$

We have: .$\displaystyle (\overline{X \cap Y}) \cap Y \;=\;(\overline X \cup \overline Y) \cap Y$

. . . . . . . . . . . . . . . .$\displaystyle = \;(\overline X \cap Y) \cup (\overline Y \cap Y)$

. . . . . . . . . . . . . . . .$\displaystyle = \;(\overline X \cap Y) \cup\; \emptyset$

. . . . . . . . . . . . . . . .$\displaystyle = \;\overline X \cap Y$ . . . answer (a)