Indexed Version: Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be a set. Prove 1. ∩ i∈I Ai ⊆ Ak for all k∈I. If B⊆ Ak for all k∈I, then B ⊆ ∩ i∈I Ai.

Q: U = {7, 8, 9, 10, 11, 12, 13}, A = {7, 8, 9, 10}, B = {7, 8, 11, 12}, and C = {9, 11, 13}. List all…

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Q: 2/7,545

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Q: I Let A = {1,3,5,7}, B = {1,2,3}, C = (6,7} and suppose the Universal set is U = {1,2,3, ..,7}. List…

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Q: Indexed Version: Let I be a non-empty set, let {Ai}i∈I be a family of sets indexed by I and let B be…

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Q: Sets A and B are both subsets of U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and defined as follow A = {x €…

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Q: R= {(a,b)|a E T,b e T, a has higher GPA than b}. Why?

A: No, it is not a poset.  Since we know that a relation is a poset if the relation is…

Q: I don't understand why you put Ui element of I. I think you made a mistake. Please let me know.…

A: Step 1:Step 2:Step 3:Step 4:

Q: Let X = {v, w, x, 16, 17, 18), Y = {w, y, z, 16, 18, 20), and Z= {w, y, 17, 18, 20). List the…

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Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: Q1 Let U : Determine the following. {1, 2, 3} be the universal set and let A = (1, 2}, B = (2, 3}…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Identify each condition as (1) Intersecting, (2) Subset, or (3) Mutually Exclusive. Refer to the…

A: A pack of card has 52 cards of which 26 are red in colour and 26 are black in colour. 13 Diamond…

Q: Let S be the universal set, where: S= {1, 2, 3,..., 18, 19, 20) Let sets A and B be subsets of S,…

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Q: Prove or give a counter example, let A and B be sets. Then P(A∪B) = P(A)∪P(B)

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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 U = {1, 2, 3, 4, 5} be the universal set. Let A = {1, 2, 3}, B = {1, 3, 5}, and C = {2, 4, 5}.…

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Q: Let D=​{2​,5​,7​}, E=​{2​,4​,5​,6​} and F=​{1​,3​,4​,5​,7​}.   List the elements in the set D∪E.…

A: Given that      D = {2,5,7}      E = {2,4,5,6}   and       F = {1,3,4,5,7} Here we have to find the…

Q: Which of the following is true for all sets S and T? Select one: O A. SOT SOT B. SOT SUT C. SUT SOT…

A: see below the answer and explanation

Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: U={1, 2, 3, 4, 5

A: *Note: As per policy only first three parts are answered. Given: U={1, 2, 3, 4, 5, 6}​, A={3, 4,…

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

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Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: Find an example of a set A with |A| = 3 which contains only other sets and has the following…

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Q: Set U is the set of farms in a certain country. Set A is the set of farms in the country that…

A: Given that , U = Set of farms in a certain country A = Set of farms in the country that produce corn…

Q: The empty set o is open set ylgn O İhi O

A: See the detailed solution below.

Q: SETS Prove that X ⊆ Y if and only if X ∪ Y = Y.

A: Draw a sets of X and Y and plot different cases and check all conditions having XUY=Y.

Q: Let A and B be any sets. Show that: (a) A – B, B - A, and An B are disjoint with each other. (b) A =…

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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: Let A and B be nonempty sets. Prove that A x B = B x A if and only if A = B.

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Q: Let U = {x | x is an integer and 0 < 6x < 60} be the universal set that contains the following…

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Q: Let A = {Ba:a € A} be a family of sets and let G be a nonempty set. Prove GnU B.) = U(GN B.) Order…

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