Suppose A1,A2,…..A30 are thirty sets each having 5 elements and B1,B2,…….Bn are n sets each having 3 elements.Let each elements of S belongs to exactly 10 of A1,'s and exactly 9 of B1's.Then find the value of n.

If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A xx B and B xx A are : a) 2 ^(99) b) 99^(2) c)100 d)18

Let ** be a binary operation on the set Z of integers as a**b=a+b+1 . Then find the identity element:

Show that the relation R in the set A = (1,2,3,4,5} given by R = {(a,b) : |a - b| is even }, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1, 3, 5} is related to any element of {2,4}.

Let A={1,2,3} , B={3,4} . Write a relation from A and B having 5 elements. Write its domain,co-domain and range.

The Cartesian product A xx A has 9 elements among which are found (-1,0) and (0,1). Find the set A and the remaining elements of A xx A

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the value of m and n are : a) 7,6 b) 6,3 c) 6,4 d) 7,4