Give an example of each 17 Every open set is union o f m 2) union of any open set is ol er 3) Finite un ters ection af open set a is an open sel Every open ball

Q: Prove the following set infinite: {5,9,13,17,...}

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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: Identify the following set as finite or infinite. x|x is a rational number smaller than 3} Chooro

A: Given set { x | x is a rational number smaller than 3}

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

A:

Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

Q: State the formula for the Principle of Inclusion and Exclusion for 3 sets. Draw a Venn diagram…

A: The formula for The principle of inclusion and exclusion  for three sets A |A\cup B \cup C| = |A| +…

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

A:

Q: Show that the two given sets have equal cardinality by describing a bijection from one to the other.…

A: According to the given information, it is required to show that the two given sets have equal…

Q: TION 4 If A, B, C be three sets such that Au B = AUC and ANB = ANC, then : O B = C O A = C O A = B =…

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Q: Let S be a set containing 700 elements. which is greater, the number of subsets of S having 400…

A: Let S be a set containing 700 elements. We have to justify, Which is greater, the number of subsets…

Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: Suppose (S;)jEN is a sequence of subsets of R", such that each S; C R" has ieN zero content (i.e.,…

A: Option 1, 3, 4,5,6 are true.

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: Let Gbe an open set in R". Two points x, y e G are said to be equivalent if they can be joined by a…

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball…

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: Suppose that the universal set U is the set of all even intergers from 1 to 16 inclusively and A =…

A: First we will discuss the properties of a Complement set. Complement of a set X is denoted by Xc or…

Q: The contiuum hypothesis: there exists cardinal number B such that No<ß<c صواب ihi

A: Ans : False , because

Q: Suppose S and T are infinite sets and o :s-T is afunction that is not onto May we conclude that S…

A: Given statement is false We show that by taking counterexample

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: find fundamental set of soleubions cwith d real va lues for

A: Using differential equations,

Q: 4) Using equality of sets, prove that (An B)' = A' U B'

A: we know thatA∪B=x: x∈A or x∈BA∩B=x: x∈A or x∈BA'=x:x∈U, x∉A=U \ AWhere U is a universal set.That is…

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: yoint each. On the Cverage. Une jaint defectuve to be free from i How moy defective joints in a gets…

A:

Q: 8. Give an example to show that the arbitrary intersection of open sets is not an open set. 9. Give…

A:

Q: n so is {A} but do NOT use an the argu

A: To prove that if A is a set then so is A.

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

A:

Q: The set Z of all integers is countable i.e., there exists a one-one onto map Ava between the set of…

A: Note: Z = {0, 1, -1, 2, -2, 3, -3, 4, -4, ...} And N = {1, 2, 3, 4, 5, ...}

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Determine if the union/intersection of two open sets is always open then determine if the…

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Q: The infinite in tersection of -pon Set is ofen set.

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

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Q: 15. We have seen that an infinite set can be put into a one-to-one correspondence with a proper…

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Q: Let {S,},EN is a disjoint seqeuence of measurable sets , then: HUS,

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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: Let Gbe an open set in R". Two points x, y = G are said to be equivalent if they can be joined by a…

A: Solution:-

Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A:

Q: How to Apply the Archimedes'principle to prove that a set is empty

A: Consider the given information. the Archimedes' principle is defined as, Property states that for…

Q: disprove the following AUB s connected set then either A set prove on or B is conniedted

A: Since it is a multiple questions. As per our company guidelines, we have to solve the first one. For…

Q: The union of a infinite number of closed set need not be a Closed set Open Set Both open and close…

A: The union of infinite number of closed sets is

Q: Which of the following statement is not true? * Disjoint set is a set which contains all objects.…

A: Disjoint set is the set which do not contain common points

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: Show wheatear an open interval (m, n) is a union of a countable collection of closed sets or not.

A:

Q: One of the theorems is called well-ordered theorm: .a For any set A ,we have |A|<|P(A)| .b If S is…

A: The well-ordering theorem, also known as Zermelo's theorem, states that every set can be…

Q: Give example for following 1/ set is not compact

A: Compact set:- A set S⊆R is called compact “if every sequence in S has a subsequence that converges…

Q: The union of the universal set and any of its subset is * none of the choices cannot be determined…

A: our objective is to conclude

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: Suppose the universal set contains the natural numbers that are no more than 20. Sets A and B are…

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

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Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .