Choose any that is a subset of the set (Ø} {{Ø),0} {{1}}

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

A: (d) Let, x ∈ (A')'       => x ∉ A'       => x ∈ A      So, (A')' ⊆ A. . . . . . (I)…

Q: Use the element method and contradiction to prove that for all sets S and T S Ռ ( T - S) = {  }

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Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Let A be a nonempty set and let R1 and R2 be equivalence relations on A. For each x E A, describe [x…

A:

Q: An indexed family of sets (Alhet is said to be a cover of a set X if and only if X CUieIA . Use this…

A: It  has been given to us that  X⊆∪i∈I{C}i and X⊆∪j∈J{D}j. We need to show that X⊆∪(i,j)∈I×J{Ci∩Dj} .…

Q: Prove it. Establish the mapping 7 and IN.

A:

Q: Prove a neighborhood is an open set

A: Recall that, a neighbourhood of a point is a set of points containing that point where one can move…

Q: Let S be the set S={(x+y) l 2x+3y>=(greater than or equal to) 12} What would be Sc  (S complement)…

A: The given set is: S=x,y∈ℝ2 | 2x+3y ≥12 Cleary S⊂ℝ2.

Q: Define a set X by • 4 EX If a E X, then -x-12 € X - x² € X Prove that every element of X is…

A: A Well defined collectipn of object is called set. Define a set X X = { 4, -16 } 4 belongs to X -4…

Q: In the Axiom Systems section of the Background chapter (1.6), a binary relation <on a nonempty set X…

A: Given X is a set consisting of 64 teams.  Let ⩽ be the relation on X such that for a,b∈X, a≤b…

Q: Give an example of a set X and topologies T1 and T2 on X such that T1 union T2 is not a topology on…

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Q: Show

A: We prove this statement by using definition of Borel Set.

Q: Determine which of the following subsets of R are well-ordered

A: A well-ordered set is a partially ordered set in which every non-empty subset has a least…

Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: Suppose R and S are symmetric relations on a set A. Prove that RoS is symmetric iff RoS = So R.

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Q: Let S be a set, P(S) is the powerset of S, and let T be the set of all functions from S to {0,1}.…

A: Let S consists of n elements.  Then, P(S) denotes the power set of S which is the collection of all…

Q: Show that if G has no even cycles, then each block of G is either K1 or K2 or an odd cycle.

A: A thorough explanation is provided below.   Explanation:

Q: Suppose that X is a set and {A. : a E I} is an indexed family of sets (which contains at least one…

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Q: Prove that T is the discrete topology for X iff every point in X is an open set

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Q: of the cantor Show That measure set C is Zero.

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Q: From the list below, choose ALL sets that have g as a member. {{ø}} O (0} U{Ø} O (Ø)-{{Ø}}

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Q: If B1,..., Bn is a finite open cover of a compact set A, can the union B1 U... U Bn equal A exactly?…

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Q: If M and N are two norms on space X then prove that M and N are equivalent if and only if a subset…

A: Any two norms M and N on a norm space is called equivalent if  M≤N≤M. in the given question we have…

Q: Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A…

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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: We have G be a o-algebra of subsets of a countable set Y such that for every distinct x, y € Y there…

A: We know, If G is σ-algebra , then by definition of σ-algebra ϕ∈G If A∈G then  AC∈G Countable union…

Q: For any set A and any ≥0, there exists an open set O such that A CO and m* (0) ≤m* (A) + €.

A:

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: (a) |([10]² – {1,3} × {2, 5, 6}) — {5, 7, 9} × {8, 10}|.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A is a non-empty set. Show that the power set of A is in one to one correspondence with the set of…

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Q: Let 2 be the universal set and let G= p(2) the power set of 2 Define the follov operations X+Y =…

A: Given: Let's take Σ as the universal set and let G=ρ(Σ), the power set of Σ. X+Y=X∪Y;XY=X∩Y;Xc=X.

Q: Give an example of a closed subset S of R2 such that conv S is not closed.

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Q: Suppose E is a bounded, nonvoid set of real numbers. Define |E| to be the set { x: x = E}. Is it…

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Q: A is an ordered pair (G,*), where G is a nonempty set and is a binary operation on G.

A: We can solve this as follows: