Sets-Using De Morgan's Law

mcdonagh521

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

Thanks.

token56

mcdonagh521 wrote: »

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

Thanks.

Not sure we are allowed dish out answers off the bat so I will try to help without giving doing it out fully.

First step is to break up
______
(X n Y), using de morgans theorem,

you then need to use the distributive law, i.e.
A n (B u C) = (A n u (A n C) and work it out from there

Fremen

Draw a Venn diagram, it'll help you get your head around it.

LeixlipRed

Yep, Venn Diagram should help you out. Identify X intersection Y, then it's compliment then that compliment's intersection with Y. Should be easy to see what the answer is then.