Show that `A ∩ B = A ∩ C` need not imply `B = C`.

Show that A ∪ B = A ∩ B implies 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 .

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 if A ⊂ B , then C – B ⊂ C – A .

Show that if f: A to B and g: B to C are onto, then gof : A to C is also onto.

Show that if f: A to B and g : B to C are onto, then gof A to C is also onto.

Show that if f : A to B and g: B to C are one-one, then gof: A to C is also one-one.

Show that if f: A to B and g : B to C are one-one then fog: A to C is also one-one.

If A' = [(2,5),(2,1),(-3,2)], B = [(2,-1,-2),(4,0,5)] and [(4,5,2),(0,1,4)] find A + B and B -C , show that A + (B -C) = (A + B) - C .