CSCI/MATH 2112 University of Missouri Discrete Structures Problem Sets

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Problem 1 (4pts): The following sets are written in the set comprehension notation. Please list theirelements explicitly, e.g., {x | x ? N, x < 4} = {0, 1, 2, 3}.• {x | x ? N, x is even and x is prime}• {x | x ? N, x is even and x is odd}• {S | S ? Pow({0, 1, 2, 3}), #S = 2}• {A | A ? Pow(N), #A = 1}Problem 2 (3pts): The set {2, 4, . . .} is ambiguous. It can mean at least three different sets. Pleasedescribe three different sets using the set comprehension notation.Problem 3 (3pts): Find the power sets of the following sets.• {6, 7, 8}• {?}• {?, {?}, {?, {?}}}Problem 4 (8pts): Suppose A, B, C are sets. Are the following statements true? If it is true, give anexample. If it is not true, give a counter example.• A ? (B ? C) = (A ? B) ? C.• A × (B × C) = (A × B) × C.• If A ? B and B ? C, then A ? C.• A ? B ? A. …..