Problem 3. The characteristic function x, of a crisp set A is analogous to the membership function of a fuzzy set, and is defined as follows: X(x) = lifxeA =0 otherwise Using isomorphism of crisp sets and binary logic, show that Xx = 1-XA X AUB = max (XAXB ) XAMB = min ( XA, XB) XAB(X, y ) = min 1, (1- XA (x) + XB(x)} where A and B are defined in the same universe X, except in the last case (implication) where A and B may be defined in two different universes X and Y. What are the implications of these results