Let X = {a, b, c, d,e} and let T = {X, ø, {a}, {a,d}, {a,e}}, then * %3D (X, T) is not Hausdorff but it is connected O (X,T) is Hausdorff and connected (X, T) is neither Hausdorff nor connected (X,T) is not connected but it is Hausdorff

Q: Q2) Let (A,T)be topological spaces; i=1,2,3. Then A, x A2 x Az is homomorphic to (A, x A2) x A3 I

A: Definition : Let X and Y be spaces, and let B be the collection of sets U × V , where U ⊆ X and V ⊆…

Q: Let 2 v = w = and 0 = 3 Which of the following sets are linearly dependent? Select all that apply.…

A: Solution:Given vectors are      v→=203     ,  w→=111   ,  0→=000

Q: 3A Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(x1,X2,X3),…

A: The definition of inner product is given. We have to find the matrix representation of the inner…

Q: Let B={(1,-2,1), (4,-7,5), (5,-8,8)], and x=(-6,10,-7) Find [x]B

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Q: Let U​ =​{1, 2, 3, 4, a, b, c, d, e​}, E​ =​{1, 3, 4, c, d, e​},F​ =​{1, 2, b, c​}, and G​ =​{1, 2,…

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Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

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Q: Let L : V → W be a mapping, where V and W are vector spaces. Which of the following is NOT always…

A: Let L:V→W be a mapping, where V and W are vector spaces. We have to find the false statement of the…

Q: Find the area of parallelogram ABCD with vertice A(7,5,2), B(-1,2,9), C(6, –3, -4) and D(5,7,3).…

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Q: If (X,7,) and (X,7,) T. - spaces, then (X,7,nt) is also a T,- space. GOOD LUCK

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Q: Calculate the volume of the parallelepiped spanned by u = (2,0, 4), v = (2, 4, 2), and w = =…

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Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 >2 thats why it is equal to 4c^2+2

Q: Show that the set of all pairs of real numbers (x, y) with the operations (X1, Y1) + (x2, Y2) = (x1…

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Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: Given the Euclidean inner product space (R³(R),+,,*), where for each x=(x1,x2,X3), y=(yı,y2,y3) ER³,…

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Q: Let u= (1, 1, 4, 5), v = (1,4, -4,9) and w = (3, 1, 2, 3). Evaluate: a) dx2 dx3dx4(u, v, w) = b)…

A: Step 1: Step 2:

Q: Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are…

A: a) Given that v1=-2,2,1,v2=-8,7,4,v3=-29,25,14,w=6,6,1. It is required to find whether w is in…

Q: (2) Let aj = (1,2, -1), a2 = (3,0, 1) and bị = (-1, 10, 7), b2 = (1, 2, 0) in R³. %3D (a) Is a, in…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.