is the set [5,100] compact?

Q: The set having elements of the complement of the set A will be,

A: We need to find out complement of A.

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

A:

Q: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

Q: .State all the subsets that apply to /2. Include an explanation supporting why v2 belongs in each…

A: Consider the given expression, 2 the value of the given expression will be, 2=1.4142135624 it can be…

Q: Let S be the universal set, where: S = {1, 2, 3, .., 23, 24, 25} >....

A: Given…

Q: Find the dimension of the set S= {(2, 4), (4, 8)}?

A: The dimension of the set S can be find out by finding the linearly independent vectors in it.…

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A:

Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

A:

Q: The set of elements common to both set A and set B is called the of sets A and B, and is symbolized…

A: The set of elements common to both set A and set B is called the ________ of sets A and B, and is…

Q: Use the roster method to list the elements in the set: {x|x is a whole number less than 4}.

A:

Q: The set of elements that are members of set A or set B or of both sets is called the. of sets A and…

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

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

A:

Q: Prove that (2,5) is an open set

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Q: Determine whether the following are spanning sets for R2:

A:

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Show that the countable collection B = {(a,b) × (c, d)| a <b and c< d,

A:

Q: Is the Cantor set closed? Is it compact? Explain!

A:

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

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

Q: Does the set S = span M22?

A: The given set is S=1100, 0011, 1001, 0111. Note that the above set is linearly independent set.

Q: A universal set U with 117 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A:

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: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

A:

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Show by membership that for all sets A, B and C: А - (AnB) CА - В

A:

Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: What is meant by Union of sets?

A:

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

A:

Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

Q: Select the regions that correspond to the set AN BNC°.

A:

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

A:

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

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: It is the selection of objects from a set.

A: This is the problem of combinatorial. finite math, counting.

Q: 7. Show that the Obenchain class LOb(B) is a convex set.

A: Given: To show the Obenchain class LOb (β) is a convex set is given as,

Q: Construct a family of sets that demonstrates R is not compact

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Q: 5. Show that a finite set is a closed set.

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Q: prove that the union of a countable set and an uncountable set is uncountable

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Q: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

A: The set of elements that are members of set A or set B or of both sets is called the_____ of sets A…

Q: What will be the cartesian product of three sets if one set of them is empty?

A: The answer is given as follows:

Q: Are the sets Z x Z; ((x.y): x*y?) closed in (R , | |) ? What about the sets (0,1]U(2,3); [0, 00) in

A:

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: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C. If B is 4…

A: A universal set U with 17 elements has been partitioned into three subsets, A,B, and C.

Q: Does the set span R3?

A: s=310,0-11,12-1Let v1,v2,v3 in R3 , if span(v1,v2,v3)=R3 then v1,v2,v3 are linearly independent.Rank…

Q: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

Q: Show that the union of two sets, each of measure zero, has measure zero

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.