Let A and B be sets. If `A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X` for some set X, show that `A = B`.

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = φ .

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

Using properties of sets, show that A ∪ ( A ∩ B ) = A

Let A and B be two non- empty subsets of a set X such that A is not a subset of B .Then

Let A and B be two sets such that n (A) =3 and n(B) =2, If ( x,1) ,( y ,2) (z,1) are in A xxB find A and B where x,y,z, are distinct elements

The negation of the statement "If x in A nu B then x in A and x in B " is

The negation of the statement "If x in A uu B then x in A and x in B " is

Let A and B be two sets such that n(A) =3 and n(B) =2. If (x, 1), (y, 2), (z,1) are in A xx B, find A and B, where x, y and z are distinct elements.