यदि A और B दो समुच्चय हो ताकि `A nn B =A` तो `A uu B`

A uu B = A nn B iff :

Prove A nn B=A and A uu B=A rArr A=B

If A uu B = A uu C and A nn B= A nn C , then

Let A, B, and C be the sets such that A uu B = A uu C and A nn B = A nn C . Show that B = C.

A uu B = (AB) uu (BA) uu (A nn B)

Show that for any sets A and B, A = ( A nn B) uu ( A -B ) and A uu (B-A) = (A uu B)

For all sets A and B, (A - B) uu (A nn B) = A .

For all sets A and B, (A - B) uu (A nn B) = A .

Let A and B be sets. If A nn X = B nn X =phi and A uu X = B uu X for some set X, show that A = B. (Hints A = A nn (A uu X) , B=B nn (B uu X) and use Distributive law )