3. Let X = {a,b,c ,d, e}, f ={{a,b}.{b.c}.fc.e}.fe}}cP(X) Find the topology z on X generated by B.

Q: Let C be the line segment joining A(1,1,1) to O (0,0,0). A parameterization

A: Given that A(1,1,1) and O(0,0,0) Find a parameterization

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: Choose the correct answer and attach the details of your work. 1. Let X = {1,2, 3, 4}. A topology on…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let X:= (a, b.c), n=(1,2,3.4), Ty:= (0,Y, {1,3), [3,4}, {3), [1,3,4}}. Let fx-Y. f:= {(a,3). (b, 3).…

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Q: -Use Cauchy- Riemman eauadiane to shaw that euch of there tiers is entire. a fizlasxy ti(zy-x) b.…

A: Note: we answer up-to 3 multiple subparts. Please resubmit question which you would like to get…

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: Question 3. Consider the topology r= {X,ø,{a},{a,c},{a,b,d}} X = (a,b,c,d). Let A= {a,d}, find A and…

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Q: Sketch the grafph Following Funcfions Tor the :も L) 2=4- y bx+2y t3でンと *)モ x3+ +y2

A: Here we have to sketch the graph for the following function. i) 6x2+2y2+3z2=6j) z=x2+y2k) z=x3+y2L)…

Q: is absolutely and uniformly conyergent for all vlues of x an t in the circle 121 <B-¹

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Q: Let X:= {a, b, c}, Y:= {1,2,3,4}, Ty: = {0, Y,{1,3}, {3,4}, {3}, {1,3,4}}. Let f:X → Y, f:= {(a, 3),…

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Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Let (X, Ox) and (Y, Oy) be affine varieties over K. Recall that we have constructed the affine…

A: Given: Let (X, OX) and Y, OY be affine varieties over K. Now, we have constructed the affine variety…

Q: of all Z € C that z iz e = e a Descnibe and sketch the set

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Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: O Let X,X. X3 beasamPle of size n=3From the Bernolli Pmf Assune Ti ヒ(X、メ,メ) X、+メz+Xg and こ I= X,X t…

A: Using the Neymann factorisation theorem we can find out the sufficient statistic.

Q: In which of the following cases is the mapping x: R² → R³a patch? (а) x(и, v) — (и, uv, v). (c) x(и,…

A: A mapping defined from x : R3 to R2 is defined a patch if x maps U diffeomorphic ally onto x (U) As…

Q: 12, Show that ()() = (OC)- n-m' %3D 13. Show thet (A)

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Q: Con sider X={,2, --., 106? togcther with the largest 8-algebra p(X). capower set of x). Define 1 if…

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Q: 2. Let z₁ and 2₂ be two distinct points in CU{∞} that are symmetric with respect to a circle I.…

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Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: 10. Let ro = all points (x, y, z) for which (xo, yo, zo) and r = (x, y, z). Describe the set of %3D…

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

Q: Question 3. Consider the topology 1={X,.{a),{a,c),{a,b,d}} X = (a, b,c,d). Let A = {a,d}, find A and…

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Q: 5. Let H= [ (û ¿)I a,b,c EIRI, show that: (H,+) is a sub gromp of (M,+).

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: Question 1. Let ACX. Show that 1= {UcX:AcU}U{®} is a topology on X.

A: For a set X having certain collection of subsets represented by τ will be a topology on X if it…

Q: be chown that y,= é" and can e are Jolutions to the diffierential ニ equatiune dy dy 4. w Cy, yz)= ?…

A: Given- It can be shown that y1 = e2x and y2 = xe2x are solutions to the differential equation d2ydx2…

Q: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Which of the following is not a base for any topology on R? O {(-0,a): a E (-∞, 0]}U{(0, ∞)} O {(a,…

A: Base for a topology: Let X, τ be a topological space. A collection of open sets B is said to be base…

Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

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Q: Suppose that X,Y, Z CU. If n(U)= 37, n(X) = 19, n(Y) = 11, n(Z) = 16, n(X nY) = 8, n(X n Z) = 12,…

A: NOTE: A is X, B is Y and C is Z.

Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: Let Á = ry?a, + x³yzay, Evaluate A. dl along the path y = x2 from a(0,0,2) to b(3,9,2) Select one: O…

A: We will find out the required value.

Q: Consider IR and define Tę and E where I is the tepolagy cofinite topology and Ic is countable then…

A: Consider τp is co-finite topology and τc is countable topology. Assume, τp to be, a,b|a&lt;b And τc…

Q: Tofology 2. EX しT X={12/3/4 /5,6 T=Eメ,中っをり,立る, りろ4。 LeT {1,3,4), Topology ? زژه اوم.

A: For the given statement

Q: c If in is an involution of X, show that (r, y)" = (yi", xi") is an involution of X2). %3D

A: Given X is a lattice. Given in  is an involution of X To show: ((x,y)in=(yin,xin) is an involution…

Q: Let V =(1,2,3,4),V=(0,2,t,3) and w=(!,!,,1) 1. Find t so that u t v and w are to each other. or…

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Q: 3. If X = {a, b, c, d, e, f} and T is the discrete topology on X, which of the following statements…

A: True statements are: (a), (d), (g), (i), (l), (o).

Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

Q: In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx € R, fa (x) = ax.…

A: The given map is fa:ℝ,+→(ℝ,+), defined as fa(x)=ax, ∀x∈ℝ. We have to check the following: (a). Is…

Q: Let the set 7 be the union of the line segments from (1, 1) to (1,3), from (1, 2) to (2, 2), and…

A: Givan that H is the union of line segment  H = { from (1,1) to (1,3), from (1,2) to (2,2), from…

Q: A mapping f:C→ C is called bounded, if sup |f(2)| < o0. zEC Show that sin, cos : C →C are unbounded…

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Q: Let (X,Ox) and (Y,Oy) be affine varieties over K. Recall that we have constructed the affine variety…

A: Let X, OX and Y, OY be affine varieties over K . In general the tensor product of two affine…

Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

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Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

A: