Let S = {1, 2, 3, 4, 5, 6, 7, 8}. (a) How many nonempty subsets of S are there? (b) How many subsets B of S satisfy the property that {1, 8} ⊆ B? How many subsets B of S satisfy the property that {1, 8} ∩ B = ∅? (How are subsets in the first question related to subsets in the second question?) (c) How many sets B satisfy the properties that B ⊆ S and |S| = 3? (d) How many subsets of S are there with exactly three elements, at most one of which is even?

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange…

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A: We have to answer questions based on simple set theory.

Q: Let U =  {2, 3, 4, 5, 6, 7, 8, 9},   A =  {3, 5, 7},   B =  {2, 3, 6, 9},  and C =  {2, 4, 8}.…

A: Given U = {2, 3, 4, 5, 6, 7, 8, 9},   A = {3, 5, 7}, B = {2, 3, 6, 9}, and C ={2, 4, 8}. Find  (A ∪…

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Q: Let U = {3, 4, 5, 6, 7, 8, 9, 10},  A = {4, 6, 8},  B = {3, 4, 7, 10}, and C = {3, 5, 7} . Find the…

A: It is given, U= {3,4,5,6,7,8,9,10}.

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Q: (2) Is the set {r € Rr² € N} countable? Justify your answer.

A: Yes the set A={x €R : x2 €N } is countable

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Q: I need help with these two questions.

A: Detailed explanation:

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Q: 3. Find a subset of P({1,2,3}) with four elements.

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