SET THEORY - PROBLEMS In competitions

SET THEORY Problems for Engineering Competitions 1. Let R be the real line. Consider two subsets of the plane RXR: S = {(x,y): y= x+1 and 0< x < 2 } T = {(x,y): x-y is an integer } Discuss equivalence property of S and T. 2. Let f: N ---Y be a function defined as F (x) = 4x + 3 where Y= { y Є N: y = 4x +3 for some x belonging to N } Show that f is invertible and find its inverse. 3. Let A = {X: X <9, X Є N } and B = { a,b,c} be a sub set such that (a+b+c) is a multiple of 3. What is the largest possible no of subsets like B? 4. Let A = {-1,2,5,8} and B = { 0,1,3,6,7} and R is a relation ‘one less than’ from A to B. How many elements will R contain? 5. If n (A) = 115, n (B) = 326 and n (A-B) = 47 then what is n (AUB) equal to? I