Show that multiplication of two Dedekind cuts in ℝ ≥0 is commutative and associative.

Q: 2. Use an edge-counting argument to show that K, cannot be drawn on a 2-holed torus without edges…

A: Suppose K9 had a 2-cell embedding in the torus. Then, this embedding has v=9 vertices and…

Q: Consider the partial order with domain{3,5,6,7,10,14,20,30,60}and with x ≤ y if x evenly divides y.…

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Q: The fourth left-endpoint in a partition of [0, 3] with Ax = 0.5 is

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Q: 4. Find the lungth of le chord amd'its distane from the ankr. A 2.

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Q: Find the projesiin Fisi+2j intro - Scaher componet

A: The vector equation is F=5i+2j. The vector equation is v=i-3j

Q: QUESTION 1 Is y-Vy a polynomisl?

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Q: Suppose you are given four natural numbers w, x, y,z e N such that w>x and y > z. Show that ly – w|…

A: It is given that w, x, y, z are natural numbers such that w>x and y>z. Now we want to show…

Q: (d) Show that {^} is not an adequate set of connectives.

A: (d) These are necessary and sufficient conditions for a set of connectives to be adequate. If a set…

Q: Prove that a square maximizes the area of all rectangleswith perimeter P.

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Q: 4. Show that =N} which is subset of R is not compact by describing an open cover for n it that has…

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Q: 2) Show that the digital line topology on Z is not Hausdorff.

A: Given that Digital line topology on ℤ, we have to prove that it not Hausdorff Therefore, Let a space…

Q: When the class limits 4.75555 – 8.85555 are given then which of the following would be its class…

A: When the lower limit of the 2nd class is subtracted from the upper limit of the 1st class and then…

Q: is optimal a unique of

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Q: A line is a collection of _______ along a _______ path that extends endlessly in bothdirections.

A: A line is a collection of _______ along a _______ path that extends endlessly in both directions.

Q: 1. Let F be a forest with 50 vertices and 35 edges. How many trees does have F.

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Q: Prove that that any Sume with TH Convex Polyhedron has two faces of edges number

A: Let F be the face with greatest number of edges ,suppose n. There will be exactly 'n' other polygons…

Q: Describe a sequence of transformations can be used to map AJKL onto APQR? K

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Q: Prove the following 1. Show that in a line there exists an infinite number of points.

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Q: 3. By using minimal spanning method, connect this 10 areas & indicate total needed 7 5 5 5 3 3 2 7 6…

A: Use minimal spanning tree method to find the minimum spanning tree of the given graph. Let us start…

Q: At Lana's bake sale, 2/3 of the brownies were purchased by 5/7 of the customers. If there were at…

A: Let X be the number of brownies and Y be the number of customers. It is given that 2/3 of the…

Q: let (RiZ) be the usual top on et B-1 ineN] Find B.

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Q: Prove than any pair of elements in H can be mapped to the positive y-axis by an element of SL(2, R).

A: According to the given information, it is required to prove that any pair of elements in H can be…

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: If (A, B) is a Dedekind cut of Q, then B always has a smallest element. True False

A: Dedekind cut of Q :  Dedekind cut is a partition of the rational numbers into two sets A and B

Q: How many distinct linear arrangements can be made by using the following shapes?

A: The number of shape are given above in the question.

Q: Find the the Geneval partial differen tial चण Egluation xp-YP =Z

A: A differential equation which contains partial derivative of atleast two different variable is…

Q: Prove that interval [0,1] is uncountable.

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Q: 2 Reciangle AlCD with verlices A(-3,01,2C2.0), and tor 粉

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Q: will be prepared using i= 0.5, the lowest clas 18. The true limits or the class boundaries of the…

A: 18 From the part 17, the lowest class interval is (6.4, 6.9).

Q: . Give the Dedekind cuts in R 20 corresponding to the following. Your definition should not refer to…

A: Given: 10 23 23+3 To find: Dedekind cuts in ℝ≥0 for the given real numbers.

Q: Prove or disprove that AS is congruent to SB (or that CS divides AB equally) if a line is drawn from…

A: Given, in △ABC, AB=AC=aBC=bBD=CDAD=h (altitude) To prove: CS does not divides AB in two equal parts.…

Q: graph'the Sorution to the follow imy inginequratityon animber line nur (x-2) (x+5) z O

A: Solving the problem by doing the graph.

Q: Show that if α and β are Dedekind cuts, then so is α + β = {r1 + r1 : r1 ∈ α and r2 ∈ β}.

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Q: Give a proof that the associative property is a structural property. (Start with two isomorphic…

A: We have to give a proof that the associative property is a structural property. Start with two…

Q: Prove that the similarity of polygons is an equivalence relation.

A: Let A, B and C are polygons. It is known that A is similar to A and so similarity between polygons…

Q: Find c such that (5,−9)(6,3), and (c,8) lie on a line. c=

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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: Draw the Hasse diagram for the following partial order. Domain: {3, 5, 6, 7, 10, 14, 20, 30, 60}. x…

A: Hasse Diagram : For a finite poset (P,⩽), the Hasse diagram is a graph with vertices x ∈ P such that…

Q: onsider two points (x0, y0) and (x1, y1). Prove that the first order Lan￾grange polynonial is…

A: There are two points (x0 , y0) and (x1 , y1) ,now prove that the linear Lagrange interpolating…

Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: Find an increasing subsequence of maximal length and a decreasing subsequence of maximal length in…

A: GIVEN CLEAR EXPLANATION BELOW

Q: Why is it called the sandwich theorem?

A: If we have three sequences fn,gn, and hn and limn→∞fn=L=limn→∞hn then limn→∞gn=L.

Q: Exhibit an open cover of the interval (1, 2] that has no finite subcover.

A: An open cover of A is a collection of open subsets of A whose union is all of A and that a finite…

Q: If fel²() and gelices. prove that fgeles.

A: Given that f∈L2(u), g∈L2(u) By definition If  g∈L2(u)⇒||g||L2<∞

Q: • Let (A1, B1) and (A2, B2) be two Dedekind cuts of Q. Let C = A1 + A2 := {q1+q2 : q1 € A1, q2 E A2…

A: Second statement:      Let (A1, B1) and (A2, B2) be two Dedekind cut of ℚ such that 0∈A1, 0∈A2  and…

Q: 1.Determine the line limit {an} = 37 (2cos ! en

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Q: How many points and lines does a finite projective plane of order 7 have?

A: The number of points in a projective plane of order n is n2+n+1. The number of lines in a projective…

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

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Q: 1. Show that x is a regular patch.

A: given Xu,v=u2-cosv , u+sint , cosv show that X is a regular patch