6. Let A be a set. Prove there exists a unique subset B of A such that if C is of A, then BnC=C. any subset

Q: Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

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Q: Let A be a set. Prove that S = 0. SEP(A)

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

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: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

A:

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: Let B be a set and {A: aeA} be an arbitrary family of sets. Then BUn A) = %3D

A: Answer

Q: 5. Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - UB, = N(A – B,).…

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Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let A…

Q: Suppose A, B and C are sets. Prove that if A ⊆ B, then A - C ⊇ B - C

A: Dear student in the question we can't prove,  Suppose A, B and C are sets. Prove that if A ⊆ B, then…

Q: 1) Define a subset.

A: To define a subset.

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

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Q: Suppose A, B and C are sets. Prove that (A \ B) ∪ (A \ C) = A \ (B ∩ C). [Prove this using elements…

A: Suppose A, B and C are sets To proof: (A \ B) ∪ (A \ C) = A \ (B ∩ C)

Q: Let A {a1, a2, ...} and B = {b1,b2, ...} be countably infinite sets. %3D Prove that A × B is a…

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Q: Let A and B be two subsets of E. Prove using the set identities: А - В — В — А.

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: . Let A and B be two connected subset

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6. Every finite set in R is compact. Why?

A: The given question is related to real analysis. We have to show that every finite set in ℝ is…

Q: Show that every open set with respect to 7 is a union of open ball(s).

A:

Q: Suppose A and B are subsets of a universal set U. Don't use Venn Diagrams to Show that…

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

A:

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

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Q: 4. Let A be an open set in å nörmed space subset B of X .

A: Que  Ans :  Given ( X, ||-||) be a norm linear space,  A be any open subset of X    ( def- set A is…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

A:

Q: Suppose that A and B are disjoint finite sets. Prove that AUB is finite.

A: Here are given sets A and B are finite sets. Then A=m, B=n  where m, n any fixed positive integer.…

Q: Prove that A is an infinite set if and only if ∀n ∈ ω, A has a subset B such that B ≈ n.

A: given that A is an infinite set let B be any set let prove this contradiction suppose assume that B…

Q: Prove that if A is a set then so is {A}!

A:

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not ?

A:

Q: Prove that every infinite set S contains a proper subset similar to S.

A: We have to prove that every infinite set S contains a proper subset similar to S. Let X=S Let X be…

Q: 5.3.8 Prove that if A CR is a finite set, then A is well-ordered.

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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…

A:

Q: Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly

A: Set equality

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: Show that the derived set E′ of any set E is closed.

A: Here is the proof .

Q: Consider the set A = {xy : x ∈ N, y ∈ N} = {1, 2, 22, 23, 24, ...., 3, 32, 33, 34,......, 4, 42, 43,…

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Q: Let Ω be a set and A = {A ⊂ Ω : A is finite or Ac is finite }

A: given that Ω is a set and also given A ⊂Ω if Ω contains n elements  then A contains (n-1) elements…

Q: let A Set bounded belou, erove that C. inf A Inf C A ン

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Q: let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are…

A: Given that X=a,b,c. To construct two topologies that have at least four open sets. We know that in…

Q: 1. Prove the following statements about sets A and B. A B= AN Bº %3D

A: Given: Let A and B be two sets. To prove,A-B=A∩Bc

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A: To prove that  If A is a countable set and B is a subset or equals to A is infinite then B is…

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A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

Q: (4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all…

A:

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

A:

Q: Let A, B, C be arbitrary finite sets from the same universal set U. - (a) Is it true that A - B C (A…

A: SOLUTION-

Q: Consider the relation = on the natural numbers 9...24. How many sets are in the partition of 9...24…

A: As we that '=' is the equivalence relation then we have a partition with the set of the natural from…

Q: Ifs is(finite or infinite) Contable Set then prove that M*(S) ==

A:

Q: Consider the set X={a,b,c,d} construct all the possible topologies of X that have only three open…

A: Given: The set X=a,b,c,d To find:  all the possible topologies of X that has only three open…

Q: Show by membership that for all sets A, B and C: A - (AnB) CA – B

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.