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In: Advanced Math

Define our “universe” S as the region in the xy-plane that is described by S =...

Define our “universe” S as the region in the xy-plane that is described by S = {(x, y) : |x| + |y| ≤ 2 and y > −1} .

(a) Mathematically and graphically describe three sets A1, A2, and A3 taken from S that are mutually exclusive but not collectively exhaustive.

(b) Mathematically and graphically describe three sets B1, B2, and B3 taken from S that are collectively exhaustive but not mutually exclusive.

(c) Mathematically and graphically describe three sets C1, C2, and C3 that form an event space for S. Make the area of C2 equal twice the area of C1, and make the area of C3 equal to three times the area of C1.

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