uppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either provide a proof to show that this is true or provide a counterexample to sh

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A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

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Q: 5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In…

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Q: Problem 3. Express A = B as a quantified statement a) using onlyV over the universal set. b) using…

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Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: statements. (a) For all sets A, B and C, if A ⊆ B ∪ C then A ⊆ B or A ⊆ C. (b) For all sets A, B and…

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Q: (1) Prove, or come up with as simple a counterexample as you can: For sets A, B, in the context of a…

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Q: When A, B, and C are sets, A∩(B⋃C) = (A∩B)⋃C if and only if     A ∩ C ⊆ A ∩ B     C ⊆ A     A…

A: According to the given information it is required to tell that when the below statement holds.

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities…

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Q: Here is a conjecture: Card (A - B) = Card(A) - Card (B) Decide whether this conjecture is true or…

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Q: Let Aand B be non-empty sets such that |A|>|B|.If the number of elements in A∪Bis atmost 42 and at…

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Q: Let A and B be sets. Suppose that A ⊆ B. Prove that P(A) ⊆ P(B)

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Q: display that if A is an infinite set, then whenever B is a set, A ∪ B is also an infinite set.

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Q: Suppose that A and B are two sets. (a) If n(A ∪ B) = 22, n(A ∩ B) = 8, and n(B) = 12, find n(A). (b)…

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Q: (a) Let A, B, and C be arbitrary sets. Use an element argument to prove that A ∩ (B ∩ C) =(A ∩ B) ∩…

A: a) Given that, A,B,C are arbitrary sets. To  prove that A∩B∩C=A∩B∩C, show that A∩B∩C⊆A∩B∩C and…

Q: (1) If A is an uncountable (2) Z† × Z is a countable set. Select one of the following choices: set…

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Q: Let T and M be a non-empty families of sets with T  ⊆ M. Show that ∩T  ⊆ ∪ M.

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Q: |(A ∪ B)\(C ∪ D)|

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

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Q: 5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In…

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Q: For any sets A, B, C  use element argument to prove that  (A-B) - C is a subset of A - C

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Q: Let A, B, C be sets. (a) Prove the distributivity law: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). Your proof…

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Q: Let A, B and C all be sets with a universal set U. Prove or disprove the following statements: i. If…

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Q: Let ℱ and ? be a non-empty families of sets with ℱ ⊆ ?. Show that ∩ℱ ⊆ ∪?.

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Q: Consider the following statements about subset relations between sets: i. N ⊆ Z ii. R ⊆ N iii. Z⊆R…

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