The characteristic function XA of a crisp set A is analogous to the membership function of a fuzzy set, and is defined as follows: XA(x) = 1 if XE A = 0 otherwise Show that XA = 1 - XA Xavb = max( XA, XB) XanB = min (XA, XB) XA-B(x, y) = min[1,{1 - XA(x) +Xay)}] where A and B are defined in the same universe X, except in the last case (impli- cation) where A and B may be defined in two different universes X and Y. What are the implications of these results?