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…

A: Given,no.of red marbles=4no.of green mables=3no.of lavender marbles=1no.of yellow marbles=3no.of…

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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: A multiset is a collection of objects, just like a set, but can contain an object more than once…

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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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A: The solution to the question is attached in the images below.

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Q: 9. Let P denote the open sentence "x € A" and let Q denote the open sentence "x € B". (a) Write "x…

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A: Given, 2A∆2A∆B

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Q: I need help with these two questions.

A: Detailed explanation:

Q: Q26. Which subset immediately precedes the subset {X7, X5, X3, X2, X1} of the set S= {X7, X6, X5,…

A: Total number of subset of S =2^8 = 256 Now let's find subsets having 5 elements. {x7,x6,x5,x4,x3}…

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Q: {x|x<2} is (-00,2) in set notation form. O True

A: Given that: {x|x&lt;2}

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Q: Statement (11, 13, 15) Z (11, 12, 13, 14, 15} (7,9} Ø {c, d, f, g} = {d, fr (q, r, w) C (q, r, w}…

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Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 5…

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Q: 4. Let A = {a,b), B = {1,2], and C= {1,2,3), and see Definitions 2.2.4 and 2.2.7. (a) List the…

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

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Q: If A = {1} and B = {1, 2, 3, 4, 5} , then which of the following is(are) true? Choose one answer and…

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