# Sets-Using De Morgan's Law

• May 25th 2009, 07:14 AM
mcdonagh521
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
• May 25th 2009, 09:51 AM
Soroban
Hello, mcdonagh521!

Quote:

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

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

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

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

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

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

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