Thread: Prove Set theroy

Prove that for any two sets A;B , we have (A n B)^c = A^c u B^c


I think im supposed to start expansion with the de morgan laws my teacher said I was doing it wrong I'm pretty sure this is the correct approach but i dont know how to continue

Originally Posted by treetheta

Prove that for any two sets A;B , we have (A n B)^c = A^c u B^c


I think im supposed to start expansion with the de morgan laws my teacher said I was doing it wrong I'm pretty sure this is the correct approach but i dont know how to continue

Lol usually if your lecturer tells you it's wrong it's wrong...

Consider an element .

Then x is NOT contained in the intersection of A and B.

Hence x is NOT contained in A or B.

Hence x IS contained in and also .

So .


Then to prove the reverse...

Well, you try it.

so then

x is an element of A^c u b^c

hence, X is an element of A^c and B^c

so x is not contained in A or B

so x is an element of (AnB)^c since AnB is everything thats in both A and B

hence

(A n B)^c = A^c u B^c

is that the correct approach?

Originally Posted by treetheta

so then

x is an element of A^c u b^c

hence, X is an element of A^c and B^c No: x is an element of OR . This renders the rest of the proof invalid..

so x is not contained in A or B

so x is an element of (AnB)^c since AnB is everything thats in both A and B

hence

(A n B)^c = A^c u B^c

is that the correct approach?

It is the correct approach.
Now, after stating OR , separate to 2 cases:

1) If , is x in ?
2) If , is x in ?

Try to formally write this, it usually helps..