Find a topology in which the point x = 5 is an open set.

Q: 1- sketch the set of points determined by the given condition: (a) z-4+1=3 (b) 17-11 2+4 |

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

Q: Give and solve example of complete space

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Q: Define a translation and construct a geometric preimage and image on a coordinate plane to model a…

A: A translation is a transformation that occurs when a figure is moved from one location to another…

Q: 3. f(x, y) = x² x+y + y²-1 -; (1, 1), (-1, 1).

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Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

Q: Let (A= (2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72), R) be a partially ordered set, where the relation…

A: We have to find the smaller element of set. Set of all upper and lower bound.

Q: Find the value of a for which 4 1 is in the set 2 H = span -3 4 -2 a =

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Q: 4) Let a < b be real numbers. Prove that the half open/half closed interval (a, b) is both an Fo and…

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Q: Find all maximal independent sets of path Pio and C10.

A: Given: The graph P10 and C10 To find: All maximal independent set. Path: A regular curve of degree 2…

Q: y=12x³-x4 = x³ (12-x)

A: The function.To find the local maxima or minima and the absolute maxima or minima.We use the concept…

Q: Use graph to find  set. [1, 3) ∩ (0, 4)

A: Given set is  [1, 3) ∩ (0, 4) The graph of the given set is as shown

Q: Explain with an example of a topological space which is singleton that is open but not close and…

A: Example in refer of not  open but closed .Take , Here A is singletone set which is closed but not…

Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

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Q: State whether each of the following set is finite or infinite:(i) The set of lines which are…

A: :Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Show that the set given in the image below is non convex. Please prove the result mathematically…

A: A set is said to be convex if for any two points in the set the line segment joining those points is…

Q: Find all points having an x-coordinate of 1 whose distance from the point (-3, - 2) is 5. ..... The…

A: NOTE: Refresh your page if you can't see any equations. . let the (1,y) whose distance from the…

Q: H3 H4 45 45 40 H1 H6 30 75 75 20 25 H5 40 H2 45 100 90 45 80 H7 H10 50 15 H8

A: Given: A graph with 10 nodes. To find the minimal distance from H1 to any of the other nodes.

Q: If D(L AOB) states the set of points located on the OA side containing point B and the OB side…

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Q: Show that the set { 159 is linearly independent

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Q: denumerable. Apply the definition and prove that the set A = {₁, {} ... } is

A: An infinite set is denumerable if it is equivalent to the set of natural numbers I.e there is a…

Q: Show that the interval [0,1] is a closed set in R

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Q: find the equation of a locus of a point P such that distance of P from the origin is twice the…

A: Let us consider that, an arbitrary point P is x,y. Vertices of origin and point A are 0,0 and 1,2…

Q: Show that the sum of linear maps is linear.

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Q: Use graph to find set. [2, ∞)∩ (4, ∞)

A: Use the graph to find [2,∞)∩(4,∞)