There is an imprecise relationship between the ambient temperature for clay masonry bricks and their compressive strengths, Let X be a fuzzy set of fracture strengths (in units of pounds per square inch) and Y be a fuzzy set of temperatures (in degrees Fahrenheit) with the following membership functions: 1.0 0.8 0.6 + + + 1500 2175 7000 0.4 0.5 1.0 + + + + X = Y = {20 Z 0.5 12 750 1 + 0.6 0.3 25 32 50 90 105 (a) Find the Cartesian product represented by the relation R=XxY. Now, suppose we have a second fuzzy set of masonry strengths given as 0.4 0.5 + 1500 2175 0.6 0.8 + 7000 12750 0.3 16 500 (b) Find S=Z... R... using max-min composition. (c) Find S=ZR... using max-product composition. 0.1 20000 0.9 16 500 1.0 20 000