Consider the sets A and B of Example 12. Find `A ∩ B`.

Consider the sets X and Y of Example 14. Find X ∩ Y .

If AxxB={(a,1)(a,2) (a,3)(b,1)(b,2)(b,3)} find the sets A and B and hence find BxxA.

Consider the sets A ={p,q,r,s} and B={1,2,3,4}. Are they equal?

Consider the sets φ, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9} . Insert the symbol ⊂ or ⊄ between each of the following pair of sets: (i) φ . . . B (ii) A . . . B (iii) A . . . C (iv) B . . . C

Show that the relation R in the set A = {x in Z : 0 le x le 12} given by R = {a , b) : |a - b| is a multiple of 4} is an equivalence relation.

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

Consider the non-empty set consisting of children in a family and a relation R defined by a R b if a is brother of b. Then R is

Show that the relation R in the set A={x in z, 0 le x le 12} given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.

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

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).