(a)Given set A={honest,violence} and B={peace,prosperity,desctruction}.Write the set `AxxB`,choose one element of `AxxB`.Which values would you like to have in your life?

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

Two finite sets A and B have m and n elements respectively. If the total number of substs of A is 112 more than the total number of subsets of B, then the value of m is a)7 b)9 c)10 d)12

(b)Suppose a set A={January,February,August} and set B={28,15,30}.Write a realtion R is given by R={(a,b) in AxxB ,Where a is month and b has number of days.Also ,find R^-1 .Which ordered pair represent an independence day?

Given a non empty set X , consider P(X) which is the set of all subsets of X . Define the relation R in P(X) as follows. For subsets A, B in P(X) , A R B if and only of A sub B . Is R an equivalence relation on P(X) . Justify your answer.

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.