Give an example of sets A,B and C such that `A nn B = phi and A uu B = X`

Find sets A, B and C such that A nn B , B nn C and A nn C are non-empty sets and A nn B nn C = phi .

If A and B are two sets such that A sub B , then what is A uu B ?

For sets A,B and C, prove that : (A-B)nn C=(A nn C)-B .

Using properties of sets, show that A uu ( A nn B)=A

Using properties of sets, show that A nn (A uu B)=A

Prove that : A nn(B-A)=phi .

For any sets A and B, prove that : P (A nn B) =P (A) nn P (B) .

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 )

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.