1. Let X = {1,2, 3, 4}. A topology on X is %3D a. T = {0, X, {1}, {2}} b. T2 = {0, X, {1}, {3, 4}} %3D с. Тз 3D (ф, X, (1}, (1,3, 4}} d. None of the above 2. Let X {1,2, 3, 4} and let T = {ø, X, {1}, {3},{1,3}} be a topology on X, then {2, 4} is %3D a. open in (X,T) b. closed in (X,T) c. clopen in (X, T) d. neither open nor closed 3. Let (X, T) be the topological space defined in question 2., then the closure of {2} is а. X b. {2, 4} c. {1,2, 4} d. None of the above

Q: Let w = xydx + 2xdy - ydz E 2'(R) and let a: R a(u, v) = (uv, u², 3u + v). Compute do, a*o, d(a*o),…

A: Given ω=xy dx+ 2x dy - y dz in Ω1ℝ3x,y,z And let α:ℝu,v2→ℝx,y,z3 be given by  αu,v=uv, u2, 3u+v. To…

Q: Find g(u(х, у, г), в(х, у, г), и(х, у, 2)) if g(x, y, z) = z sin xy, u(x, y, z) = x²z", v(x, y, 2) =…

A: Given:  (1) gx, y, z=zsinxy (2) ux, y, z=x2z3 (3) vx,y,z=πxyz (4) wx,y,z=xyz To find : gux, y,z, vx,…

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: b) Is there a linear map T: V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 1?

A:

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

A:

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

Q: 15. If t={X,Ø,{1,4},{4,3},{1,4,a},{b}} is a topology on X-{1,2,3,4}, then: * a=4, b=2 O a=3, b=1 O…

A:

Q: Let (1 0 1 0 (G : :). m = (C : :) m. = (C : ). m. = (: ) (0_ 0 o 0 1 1 (1 2 m1 = m2 = m3 = m4 = 0 1…

A:

Q: 5. Prove that the baker map 2x B(z) = 2z - 1 <z<1 is chaotic on (0,1).

A: Given the baker map, Bx=2x,0≤x≤122x-1,12≤x≤1

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),…

A:

Q: - Find the mappings taking [(0,0, 0), (1,0, 0), (0, 1,0), (0, 0, 1)] in u, v, w space to each of the…

A: Consider the given mapping U= [(0,0,0),(1,0,0),(0,1,0).(0,0,1)] in u,v,w space to  each of the…

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: Suppose that receiving stations​ X, Y, and Z are located on a coordinate plane at the points…

A: Given:X≡4,4Y≡-12,-4Z≡-6,9The epicenter of an earthquake is determined to be 5 units from X​, 13…

Q: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

A:

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

A:

Q: If (x, y) → (x + 3, y - 7)maps TUVWto T'U'V'W', what is the algebraic description that will map…

A: Given x,y→x+3,y-7 maps TUVW to T'U'V'W'. Let (x,y)→(a,b) where a=x+3, b=y-7 x=a-3,y=b+7 Therefore,…

Q: 15. Given nonempty-subsets of R², say Y1,..., Yn, let Y* = {E÷=1 Y; | Y1 € Y1,.., Yn E Yn}. Given p…

A: Given: Y*=∑j=1nyj | y1∈Y1, y2∈Y2, ..., yn∈Yn and, for any p∈R2 and nonempty subset Y⊂R2, vp,…

Q: 1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by…

A: According to our guidelines we can do only one question if multiple question are posted. Please post…

Q: 14) Find the Jacobian of the tra nsformation. x=5u-v,y=Du+3v

A:

Q: 1. Let X = {1,2, 3, 4}. A topology on X is a. T = {0, X, {1}, {2}} b. T = {6, X, {1}, {3,4}} c. T3 =…

A:

Q: 3. Suppose that {v,,v,,v,} is a linearly independent subset of R". Show that the set {v,,v, +v3,v; +…

A: The set {v1,v2,......vn} is linearly independent if for the combination, av1+bv2+......nvn=0 for…

Q: 4) Again let Universe U = {0, 1, Let S = {1,2},T = {2,4,6, 8}, R = {1, 3,5}. Give the following: %3D…

A: According to Bartleby guidelines I can only 3 subparts of the questions.

Q: 2. Let L={x,y,z}with the topology r={L,ø,{x},{x,y},{z},{x,z}}. Verify whether L is normal or not.…

A: The given problem is related with topology. Given that L = x, y, z with the topology τ = L, ϕ, x, x,…

Q: 13. If t={X,Ø,{2,4},{1,4},{1,2,4},{4}} is a topology on X={1,2,3,4}, let A={1,3,4}, then Int(A)= *…

A:

Q: , Y, 2, W) w) 3. Using methods of linear algebra verify whether Question a. span{(2,0,0), (1, 3,0)}C…

A:

Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: -5 1 Let y = -2 U2 = = In 4 -1 Compute the distance d from y to the plane in R spanned by uj and u2.…

A:

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – z, z – x, x – y), then div(curlG (x, y,…

A: given statement if false.

Q: Prove that y, + y, +2y, 56 is a valid Gomory cut for the following feasible region. X-{yeZ: 4y, +5y,…

A: We have, y2+y3+2y4≤6 X=y∈Z+4 ;X=4y1+5y2+9y3+12y4≤34X=y∈Z+4 ;X=5y2+9y3+12y4+5y2≤34X=y∈Z+4 ;…

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: 1. Let X = {1,2, 3, 4}. A topology on X is a. T = {ø, X, {1}, {2}} b. T2 = {6, X, {1}, {3, 4}} c. T3…

A:

Q: 18: Consider the two linear maps T, and T2 on V, defined as T(X, X, x) = (0, xz x) and T,(x , x, x)…

A:

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

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

Q: 10. If t={X,Ø,{2,4),{1,4},(1,2,4},{4}} is a topology on X={1,2,3,4}, let A={2}, then the closure of…

A:

Q: If o is the triangular region with vertices (1,0,0), (0, 1, 0), and (0, 0, 1), then (x + y+2) dS

A: Using stokes theorem,

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

A:

Q: 32. Let y = (1, 2, 6) and u = (1, 1, 1). Compute the distance from y to the line through u and the…

A: line through u(1, 1, 1) and v(0, 0,…

Q: 1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A:

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: Solution: The joint pmf of X and Y is  fX,Y(x,y)=(x+y)21     x=1,2,3    and y= 1,2  The pmf of X and…

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y– z, z – x, x – y), then div(curlG (x, y,…

A:

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: Assume that z = ƒ(w), w = g(x, y), x = 2r^3 - s2, and y = re^s. If g x(2, 1) = -3, g y(2, 1) = 2,…

A:

Q: Let u = (1, 1), v = (3, -2), w = (4, 3), and y = ( map from R² -3, 4). Let L be a linear | to R?…

A: We know Let  Given

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – 2, z – x, x – y), then х, х — у), then ||…

A:

Q: Let X = {1, 2, 3, 4, 5, 6} and let T1 = {X, %3D 4, {2}, {1,2}, {2,3,4}, {1, 2,3,4}} and T2 = {X, þ,…

A: If T is the topology on Set X then T contains all subsets of X.

Q: Prove that if w = f(x,y,z), x=r-s, y=s-t, and z =t-r then ôw ôw ôw + âr' as = 0. ôt

A:

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…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.