Group IV Consider a set A and a non-empty subset BCA such that #A = n and #B = k. Determine the total number of subsets of A whose intersection with B has a single element.

Q: Define a smallest possible set of which both {1,3,5} and {0, 3,4 } are subsets.

A: The subsets given are {1, 3, 5} and {0, 3, 4}.

Q: Use sets  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},   A = {2, 4, 5, 7},  and  B = {1, 3, 4, 5, 6, 9, 10}…

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Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

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Q: Find an orthogonal set with the same span (and same number of elements) as 7 -5 4 4 7 (198) -10 -8…

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Q: Let n, m 2 3. Find the number of 3n-element multi-subsets of the multi-set A = {n.a1, n.ag,..,n.am}…

A: Consider the given information.

Q: A set has 20 elements. How many subsets of the set can be formed such that each subset consists of…

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Q: Are   any   open   subsets   of   R   sequentially   compact?     Explain   why   or   why not

A: The objective of the question is to determine whether any open subsets of the set of real numbers…

Q: Construct an example of a subset B of P({a, b, c, d}) such that (B, C) is a total ordered set.

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Q: Compute the following: 1. L {t cosh (t-1)U(t-1)} 094 0911 C-₁ { 8 (8² + 4)}} 2. L-1 4033 s peque

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Q: If a universal set contains 250 elements,

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Q: Suppose that A and B are subsets of S. Express symmetric difference of A and B (AtriangleB) in terms…

A: It is given that A and B are subsets of S. The symmetric difference A and B is defined as the set of…

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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Q: Both questions below refer to set A = Z – {-2,0}. a) Give a partition of A into infinite many…

A: Solution: Definition: Let Ψ be a partion of the set A. That means, Ψ is the collection of subsets of…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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Q: Find an orthogonal set with the same span (and same number of elements) as 11 -9 -7 3 (898) 4 1 3 2…

A: Using Gram-Schmidt orthogonal process:

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

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Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Give an example of a bounded set that has infinitely many isolated points

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Q: union of a collectionm of connected sets that have a point in common is conne

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Q: Give an example of a countable collection of finite sets whose union is not finite.

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Q: If G(sub alpha) is a collection of closed sets, then the intersections of the G(sub alphas) is a…

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Q: Let A, B, C be subsets of X. show that Av (Bnc) - (AUB)n (AUC) AnCBUC) = (ANB)~ (ANC)

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Q: Show The union of a finite number of open sets in R is an open set.

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Q: A set with 6 elements has —- subsets

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