Đ A is a closed set.

Q: Write true otherwise false if the pairs of sets are equal,{{1}},{1,{1}}

A: Two sets A and B are equal if A and B  have the same elements.

Q: Thoorem: is not closed set

A:

Q: We say that a space (X, τ) is not connected if there exist two nonempty openings A, B such that A ∩…

A: Open Set: A X, τ be a topological space. Then the sets in τ are called the open sets of the…

Q: List all of the subsets of (x, y, z).

A: Given that the set x,y,z. Find all the subsets of the given set. Definition: A set is a well-defined…

Q: What is a set?

A: Definition of the set:

Q: Give an example of each of the following or explain why you think such a set could not exist. (i) A…

A: (i). Such a set could not exist. Let  be a nonempty subset of a topological space . Let . If  is not…

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: 4. Prove that if A and B are convex sets, then AN B is also convex.

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: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: True or False The intersection of two sets is always a subsetof their union

A: To check the statement

Q: Which of these sets are equal: {x, 1, z}, {z, 1, z, x}, {1, x, 1, z}, {1, z, x, 1}?

A: Given sets are x,1,z , z,1,z,x , 1,x,1,z , 1,z,x,1 find out which sets are equal

Q: Find the transitive closure of R={(0,1),(0,2),(1,1), (1,3),(2,2),(3,0)}

A: Given relation is                              R=(0, 1), (0, 2), (1, 1), (1, 3), (2, 2), (3, 0) we…

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

A:

Q: If a set A has 63 proper subsets, what is |A|? *

A: Solution...

Q: S is a nonempty set of real numbers that is bounded.

A:

Q: Give example open set is compact

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Q: show that (0.1)with usual topology is connected

A: Sol

Q: Define Closed sets ?

A: Closed sets are defined as a set which consists all of their limits points. It is also defined as…

Q: Show that if A is closed in X and B is closed in Y then A × B is closed in X × Y

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Q: why Ua equals to empty set

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Q: The cartesian product of nonempty family of nonempty sets is nonempty صواب ihi

A: The cartesian product of nonempty family of nonempty sets is nonempty

Q: Express (4, 10) as a set {x : |x − a| < c} for suitable a and c

A: Write the given interval in inequality form as follows: 4<x<10

Q: denotes the set of subsp

A:

Q: Use the listing method to express the set S = ((1,3] x {2,4}) n z².

A: Given, S=(1,3]×{2,4}∩ℤ2 We have to express it in the Listing method, As we know, ℤ2=(a,b) where…

Q: Give an example of a bounded set that has infinitely many isolated points

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Q: Use the definition of compact set to prove that the set [0,1] is compact

A: We know that a set E is compact if every open cover of E has a finite subcover. We suppose, that O…

Q: Provide an example of a topological space that is connected but not path-connected,why?

A: We use definition of connected and path connected sets. We use contradiction method.

Q: If minimum observation is 46.8 and maximum observation is 192.4, number of classes is 6, then the…

A:

Q: What is the minimum number of points that can be contained in a space

A: There is no minimum number of points to be contained in a space. But if we want to find a location…

Q: Prove that a nonempty set is bounded if and only if it is contained in a bounded interval

A: A non empty set S is called bounded if it has both upper and lower bounds, In a certain sense a non…

Q: Can you show an example of Null space?

A:

Q: i) show that a closed interval is a closed set;

A: Note: According to bartleby we have to do only first question please upload the question separately.…

Q: How different can two sets of R ^ 2 that have the same boundary be?

A:

Q: Show that any subset of bounded set is bounded

A:

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: 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: Find the cardinality of the set {x|x is an even whole number less than 10}.

A:

Q: Explain the idea of cardinality. When is a set denumerable? Show that the union of two denumerable…

A:

Q: Prove that the open ball B(p, 8) = {x : ||x – p|| < 8} is a convex set. [Hint: Use the Triangle…

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Q: Explain the Cauchy–Schwarz Inequality?

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Q: open ball is the open set

A:

Q: 2.2 Is any discrete space complete? Give an example to substantiate your answer.

A: Yes, any discrete space is complete.

Q: Show that both ℝ and ℝ2 may be covered by countably many open balls

A:

Q: Give example closed set and bounded set is compact

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: What is the possible number of reflexive relations on a set of 5 elements?

A: Introduction : We have give a set of 5 elements , we have asked for the number of reflexive…