Prove that the similarity of polygons is an equivalence relation.

Q: 4. Give a geometric description of each family of planes.

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Q: t-

A: There is two type of translation in this graph One is shifting towards right side  Other one is…

Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Show that Loo is not icomorphic to a subepace of

A: Consider the spaces l∞   and   lp where p∈1, ∞. It is known that l∞ is not a separable space but, lp…

Q: What is the natural domain?

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Q: 2. Determine whether the following multigraphs are Eulerian, semi-Eulerian or neither. Explain your…

A: Explanation we have to shown whether the given multigraphs are Eulerian , semi-Eulerian or neither…

Q: can two disjoint sets be close? Justify your answer using an example.

A: We know that any closed interval of the form [a,b] is an closed set. We use this fact further.

Q: Consider the relation on A = {a, b, c, d, e} given by R ={(a,b),(b,c),(b,d),(b,e),(d,e)} .Explain…

A: Given that, A=a,b,c,d,e And R=(a,b),(b,c),(b,d),(b,e),(d,e) The graph for the diagram is,

Q: Show that the real line is a metric space.

A: Answer is mentioned below

Q: 2. Given A, B, and C are non-collinear points, draw the following or explain why it is impossible…

A: We have given three points A,B,C  which are non colinear  that  is these three points does not lie…

Q: Consider the transformation of a rectangle ABCD to produce a rectangle DEFG. Which sequence of…

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Q: The boundary of a set is equal to the boundary of the complement) True or false

A: (The boundary of a set is equal to the boundary of the complement) True or false

Q: Describe a sequence of transformations that shows that Polygon A is congruent to Polygon B.

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Q: Let two metrics be bi-lipschitz, prove it is an equivalence relation

A: Find the attachment for the solution.

Q: Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point,…

A: Axioms3 of Fano’s geometry: The axiom 3 in Fano’s geometry is stated as “not all points of the…

Q: Prove the inequality theorem 6 which states that the sum of the lengths of any two sides of a…

A: Consider a triangle ABC as shown below.

Q: Why the order in which you list the vertices of two polygons in a congruence statement is important?

A: Answer: When naming congruent polygons, it is important that the corresponding vertices be in the…

Q: Describe a sequence of transformations that shows that Polygon A is congruent to Polygon B. B

A: Given:

Q: Stafe true andwer, your or Confinuous map en a metico is an open map

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Q: which axioms for a finite projective plane are also valid in Euclidean geometry? which are not?

A: A finite geometry is any geometric system that has only a finite number of points. The familiar…

Q: Prove that homotopy with respect to a domain 2 is a transitive property.

A: We will show that homotopy w.r.to the given domain is a transitive property.

Q: How many different size of infinity are there? How does it relate to one-to-one correspondence?

A: There are actually many different sizes or levels of infinity; some infinite sets are vastly larger…

Q: The algebraic translation of "x is at most 7" is

A: Given : The algebraic translation of " x is at most 7" is ______________ .

Q: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with the euclidean…

A: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with theeuclidean topology.…

Q: Define the Cartesian product of sets X and Y? How is this Cartesian product denoted?

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Q: Every regular space is hereditarily regular.

A: We have to prove that every regular space is hereditarily regular. Consider a regular topological…

Q: Show that an isometry of Rn is one-to-one.

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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: Assume a directed acyclic graph is encoded as a relation R. Give a concise proposition stating that…

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Q: Show that the “Relation is Congruent to” on the set of all triangles in a plane is an equivalence…

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Q: Justify the following statement: the total degree (sum of all degrees of all vertices) of a finite…

A: Isomorphic Graphs Two graphs G1 and G2 are said to be isomorphic if − There exists a function ‘f’…

Q: Prove that congruence of angles is an equivalence relation. Hint: Refer to the proof for congruence…

A: Two angles are said to be congruent if they are equal in magnitude.

Q: Define: what is an equivalence relation?

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Q: topological spaces X and Y,

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Q: Prove that in any metric space, an ɛ- eighborhood of a point is an open set.

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Q: Evaluate: (In(2x-1)- ♫ − ( ²¹ ) + 25) da - 2 Limits: [1, 6] Using Trapezoidal, n = 30

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Q: The number of equivalence relations on the set {1, 2, 3, 4} is

A: A relation defined on a non empty set S is called an equivalence relation if it is reflexive ,…

Q: If fis a bijection, find the sets X and Y.

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Q: Describe a congruence transformation that maps quadrilateral CFZD to quadrilateral BPOM

A: Congruence means same size and same shape

Q: List the coordinate pairs needed in order to turn the following relations into equivalence…

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Q: Determine if the set S is span set of %3D R2x2. Solution:

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Q: Suppose we assign every element of Z xZ (think coordinate plane) one of three colors: cyan, magenta,…

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Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

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Q: Find two examples for equivalet norms on three dimensional real space

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Q: Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the…

A: It is given that, the distance of point P from the origin is same as that of distance of point Q…

Q: Compute the adjoint of the foll

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

Q: Explain why consimilarity is an equivalence relation on M,.

A: Given that consimilarity is an equivalence relation on Mn.

Q: 5. Can somcone cross all the bridges shown in this map cxactly once and return to the starting…

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Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…