Let G= Span{2+t,6-, then dim G- Select one.

Q: A relation R defined on the set of real numbers is such that xRy and yRx = x = y: R is said to be A…

A: There are many types of relations Symmetric Asymmetric Reflexive Transitive

Q: Let u= and v= Show that is in Span (u, v} for all x and y.

A: Given u=4-1 , v=41 and b=xy. The vector b=xy is in span u,v if the system containing u,v and b is…

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: The set G = :a is closed under addition %3D 0 2a

A: Use the closure property of addition.

Q: 6. Sketch the set X = {(x, y) E R? : y<x²} on R2. Shade in the set X. %3D

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Q: Let c[o] be with metrics the Space d, (f, g) - max f(x)-gen) fen) = x2 4 gcx) =x The find d, Cf,g)…

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: 1 In the relation . If R, =1 and %3D R R R, R,%3D3, find R.

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Q: Let u be Find all t

A: Given utt=π2.uxx u(0,x)=cosx ut(0,x)=0 u(t,x)=0 for all x∈ℝ

Q: let G={2nEIJ.] show that (I, +) = (G₁.)

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Q: Show that the map T : R3 -→R? given by T (x1, X2, X3) = (x1 + x2, X3) is an open map.

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Q: Let ƒ be a mapping from [2, +∞ [to, +∞[defined by: 3 f(x) = x + = x f has a fixed point. O False O…

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Q: b) A function g:Z→Z is defined by the rule g(m, n) = m + n Determine whether it is onto or not...

A: A function f:A→B is said to be onto or surjective if for all element b∈B there is an element a∈A…

Q: Consider the set F=(-infinity, 1) U (9,infinity) as a subset of R with d(x,y)=abs(x-y). Is 9 an…

A: Let (M,d) be a metric space and let S⊆M. A point a∈S is said to be an Interior Point of S if there…

Q: Show that a set {V1, ..., Vp} in R" is affinely dependent when p > n + 2.

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Q: Let A be a non-empty set and f.g:A→A be any functions such that fog is the identity map of A. Then

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Q: If vo and V, are respectively the t-conorms that are dual to the t-norms Ao and A5 respectively.…

A: In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary…

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

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Q: Define a map t: R × R → R × R by t(a, b) = (a+ b, a - b). Prove that t is a one-to-one…

A: The solution is given as

Q: If X and Y are finite sets, prove that XY = |X|Y. Here, XY is the set of all functions from Y to X.

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Q: Give the relation R induced by the partition above on A.

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Q: The mapping T(

A: (a) Given,             T(u, v)=u2-v2, 2uv

Q: Let (X, t) be a topological space and A, B EX, then 1- (X- A)° CX-Ā 2- (X-A)° 2X-Ā 3- (X- A)° = X-A…

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Q: Let 7,V be a projection af the Vect or space. Accordling to this: Show that every Xe Im (T) for…

A: The given problem is related with projection. Given that T is a projection of the vector space V .…

Q: Let ā = (- 4, - 5) and b (- 5, 0). Find the projection of b onto ä. Round your answer to at least 3…

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Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: Determine if the map g : Q ! Q dened by g(x) = x/(x2+1) is one-to-one.

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Q: If H is a subgraph of G, then show that dg(u,v) <dí(u,v).

A: A graph G illustrates how the vertices and edges are connected. Thus a graph is an ordered pair…

Q: Does the follorin relations hip define y as a real furction of x Why," AN

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Q: If n&lt;m then every linear map T: IRn -&gt; IRm is one-to-one. Is this statement true or false?

A: The given statement is

Q: Let g be a vertical stretch by a factor of 5, followed by a translation 4 units up of the graph of…

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Q: If S. F.dr is independent of the path C joining any two points, show that there exists a function O…

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Q: (ii) Find a connected subset of R² which is not convex.

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Let A and B be sets. Show that               f : A × B → B × A such that                  f(a, b) =…

A: Given:

Q: c) given an arbitrary convex function wcx) :R"→tR, prove fhat is a convex set.

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Q: Sketch the following sets of points in the x-y plane. {(x, x^2): x is in R}

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Q: Find all maps ¢:(Z,+) → (Q*, ×) satisfying O (a + b) = ¢(a) × ¢(b) Va, b e Z

A: We derive the function from the given properties.

Q: (c) If X={1, 2, 3}. T= {4, X, {1}, {1,2}, {3}, {1,3}}. JUSTIFY whether the topological space (X, t)…

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Q: Let (X7) be a topological Space and Show that A is open and closed m (xx) iff %3D

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Q: Determine whether the function f: Z x Z -→ Z is onto if f (m, n) = .m + n

A: We will solve the problem using the definition of onto function.

Q: 3. Eliminate B and a from the relation x = Bcos(wt + a) in which w is a parameter not to be…

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Q: Sketch the set of all points (x, y) such that x + y| < e*.

A: Consider the function x+y≤ex. An absolute function is defined as x=x if x≥0-x if x&lt;0. So, there…

Q: Prove that (Co0, 11·11,) is not a Banach Space for any 1<p<.

A: We have to prove that C00,·p is not a Banach Space for any 1≤p≤∞.

Q: Let a = (- 3, – 5) and b {1, 2). Find the projection of b onto a. proj; b = >

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Q: i) List all the ordered pairs (a, b) such that aRb, for all a,beX ii) Find the maximal and minimal…

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Q: If u and v belong to the span of S, so does u+v

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Q: Give an example of (v1, V2, V3) and (W1, w2, W3) independent se- span(wi, w2, w3) and {v1, v2, v3}(…

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Q: Let E ⊆ R. Show that E is measurable if and only if χE is measurable

A: