I) We know that -5,-4,-3,-2,-1 and IN are well-ordered sets with respect to the trivial ordering. Let X=- -3,-2,-1 UN. Prove that the poset X is a well- ordered set with respect to the trivical ordering.

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: i. PROVE THAT THE EXCLUDED POINT TOPOLOGY ON ANY SET WITH AT LEAST 2 POINTS IS NOT HAUSDORFF. ii.…

A: Definition: A topological space X, τ is said to be Hausdorff if for every x, y∈X there exits U, V∈τ…

Q: Define Open set ?

A:

Q: Is the relation of “mapping” between two sets used to determine cardinality - and not used to…

A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

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Q: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

A: It is given that the universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.If A = {1, 2, 3, 4, 5} and…

Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

Q: For each condition below, give an example of a set that satisfies that condition, or prove that one…

A: The given of the question is a list of conditions related to sets and subsets of real numbers, and…

Q: Let A= {1,2,3,4,5,6} and B={2,4,6,8}. what is the cardinality of A ∩ b?

A: Cardinality of a intersection

Q: If a universal set contains 250 elements,

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Q: a) State the intersecton of an indexed family of sets.

A: According to guidelines we can do only first question thank you .we have to state the intersecton…

Q: A relation ''<'' is 1) İrreflexive. 2) Transitive. called a quasi-order on a set S if its: صواب ihi

A: We know that

Q: Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation…

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Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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Q: 5. For each pair of sets, give an explicit bijection from one to the other, showing that they have…

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Q: Show that the set is infinite by placing it in a one-to-one correspondence with a proper subset of…

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Q: (b) Let = {A; : i EN} be an indexed family of sets with the property that A₁ A₂ 22 A, 2..., that is,…

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Q: List the first four elements in order of the set { x | x = 4k + 1, and k is a natural number} (List…

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Q: Let A and B be subsets of some universal set U. Prove each of the following: *(a) An BCA * (b) A…

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Q: (1) In the universal set U ={1,2,3,4,5} we define the following sets: A ={1,2,3}, B = {3,4}, and C =…

A: Note: You have posted a question with multiple subparts. We have solved the first three subparts for…

Q: Let U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14} be the universal set. Let A = {2,3,4,5,6,7,8,9,10}. II.…

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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 U = { a, b, c, d, e, f, g, h} be the universal set. Let A = {e, g, d, a, f}, B = {b, g, c, f}…

A: (A∩B)={a,b,c,d,e,h}B−A={b,c}(B−C)∪A={b,c,e,g,d,a,f}Explanation:

Q: two example of open set in R, closed set in R, and the closure of that set

A:

Q: Determine whether the following statements are true or false: (a) The empty set ∅ is a subset of {1,…

A: Empty set is a subset of every set. A Power Set is a set of all the subsets of a set.

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: Show that the N and the set {1,3,7, 15, 31, . . } have the same cardinalit

A: To show N and the set S= {1,3,7,15,31...} have the same cardinality, we need to show there is a…

Q: Answer the following True or False. (a) {1,2,3} is a subset of {3,2, 1, 4). (b) (3,2, 1,4) is a…

A: We have to find given statements are true or false.

Q: I) We know that -5,-4,-3,-2,-1? and IN are well-ordered sets with respect to the trivial ordering.…

A: Solution: Given the sets -5,-4,-3,-2,-1 and ℕ are well-ordered with respect to the trivial ordering.…

Q: 3.) Nowe consider motrix cif possible) as a linear combination of the motrices in' ls. the set s…

A: Given that: S=3-333,3-245,6-3106To express the the following matrices in the linear combination of…

Q: Consider the "divides" relation on the set A = {1, 2, 3, 5, 6, 7, 8, 10, 20, 30, 60, 70} (a) Draw…

A: A Hassen diagram is a graphical representation of the relation of elements of a partially ordered…

Q: Suppose that U1, U2, ..., Un is a collection of n open sets. Prove that their intersection…

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Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B).

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

A: A= { 12,18,20} B = { 3,7,13,18,20} ( A U B ) is the union of two set containing all elements that…

Q: U=(4,5,6,7,8,9,10,11,12,13,14,15) U is the Universal set. A=(x)x is a natural number and 9 ≤x

A:

Q: Let U = { a, b, c, d, e, 1, 2, 3 } be the universal set. Let A = {c, e, a, 1, 2} and B = {3, e, b}.…

A: Answers are in the below box. If you have any doubts at anywhere in the explanation or answer please…