.Suppose A is an open set in R. Show that the set B= An(-10, 10| is compact, where R is the set of all real numbers and A means the complement of A in R.

Q: What set is in another class of infinity that is bigger than R?

A:

Q: Which sets are compact? The set of natural numbers less than some number M

A: We know that a set is compact if and only if it is closed and bounded. The set of natural numbers…

Q: For any sets A, and B we can write an algebraic proof to prove that A– (ANB) = OB {} A - B Bc

A:

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

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: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A:

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First we write U and the set in roaster form.

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

Q: Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A:

Q: a) Does B - A =C – A imply that B = C? Justify b) Next, does A – B = A – C imply B = C? Justify c)…

A: A-B=x∈A and x∉B = A∩Bc

Q: Write the following set in roster form: A={x:x is any two elements that belong to natural number…

A: Just observe step by step, we'll see a pattern.

Q: (4.2) For sets A, B and C, prove that (An B) x C = (A x C) n(B x C).

A: Here we have to prove that (A∩B)×C=(A×C)∩(B×C)

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

Q: display 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 and C are be sets. Show that we can have AnB= AnC without B=C

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Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: Complement: The complement of a set A is the set of elements in the universal set U that are not in…

Q: 4. Suppose A is an open set in R. Show that the set B= A°n(-10, 10]| %3D is compact, where Ris the…

A:

Q: Prove by giving an example that if any set A, g. l. b(-A) = - l. u. b(A

A: Take a set A with two elements 1 and -1

Q: If A is a subset of the set real numbers then A is a Borel set.

A: If A is a subset of the set of real numbers then A is a Borel set (True or False).

Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: Determine whether the set spans all of M2. Justify your answer with your work and/on written…

A:

Q: The closure for set P would be the set |z-(1+i)| = 2 |z(1+i)= 3 |z- (1 + i)| < 1 None of the above…

A:

Q: The empty set o is open set

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

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Find

A: First we write U as universal set. Then find complement.

Q: One of the following sets has the cardinality No : .a R .b .c {0,1,...,20} .d [0,1]

A: Cardinality of a set is defined by total number of elements in the set.

Q: Which of the following is NOT a finite set? * O A set of vowels. O {x:xE N, 1<x < 5} O (x:xe Z} O A…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 7}.  (Enter your answers as a…

A:

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

A:

Q: Given the sets : ((A∩D)∪(B∩C)) and (((A∩D)∪B)∩C):  Determine which one is a subset of the other.…

A:

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Find the complement of the set given that  U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

A: First we write U in roster form.

Q: Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable…

A:

Q: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

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Q: Suppose A, B, and C are sets. Prove that (AU B) – C C AU (B – C). - -

A:

Q: Prove: If A, B and C are sets then AU(BOC) and ((C- (AUB)) (B- (AUC))) are disjoint sets.

A: Let A, B, and C are sets. Now we prove that A∪B∩C and C-A∪B∪(B-(A∪C)) are disjoint.

Q: Show that B,(x) is open set with respect to 7 for all r> 0.

A:

Q: *· Given a set (x, x+3, x+6, x+9, x+12} where xE2*, show there exists at minimum 1 of the numbers in…

A: Given set is x,x+3,x+6,x+9,x+12 where x∈ℤ+ The objective is to show that there exists at minimum 1…

Q: Is A countable or uncountable?

A: This is a problem of real numbers properties of topology.

Q: Is this set finite or infinite? {x € R|1 < x < 2}

A:

Q: Let Cc R be a connected set and a , be R. Prove that [a , b] c C.

A:

Q: 5. Use element proof to show that for any sets A and B, if A ≤ B then A U B = B. 6. Construct an…

A:

Q: In the given questions,suppose m and n are positive integers, A is a set with exactly m elements,and…

A: Given that,                     m and n are positive integers.                    A is a set with…

Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

Q: Let A, B and C be finite sets with A C B. Suppose that B |C| =5, and that |BnC= 4. Decide whether…

A: Given: A⊂-B, |B| = |C| = 5 and | B∩C| = 4