With help of Venn diagrams show that the following are indeed true: a.X n (Y U Z) = (X n Y) U (X n Z) b.(X n Y)'=X' U Y'

Q: Given: WZ 1 bis. XY Prove: AWXY is isosceles. (Hint: This proof can be written in three steps by…

A: 2. given  WZ↔ ⊥bis XY¯ as WZ is bisector of XY XZ=ZY......(1)

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

A:

Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: Let f(x, y) = xcosy- y e*y. fry at (1,0)is equal to: -5 3 -1

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Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: Given f(z, y) = et y" - 2°y, show that fry = fyx-

A: Partial differentiation

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: Find the fowien senies fon | X), -T<X <A

A:

Q: Given z = 3 cis 120°, find z3 using De Moivre's Theorem.

A: We have to simplify

Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

A:

Q: 2. Given: XW XY, HA I WY, KB 1 WY Prove: AHWA ~ AKYB. K Y.

A: Given data is : XW¯≅XY¯ Therefore ,  ∠XWY≅∠XYW∠XWY≅∠HWA∠XYW≅∠KYBTherefore,∠HWA≅∠KYB     .....1…

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

A:

Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

A:

Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

A:

Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: 2) Given: ZRAL E LYAL, ZRLA LYLA A Prove: AR = AY R.

A: Explained below

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

A:

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: Solve the following first-order linear DE's. yE) = 1 y' + (cotx)y = xcscx, %3D

A: Proceed as shown below

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: How to solve this?

A: We are given that x + y + z = 5 where x, y, z ∈ R. Now, we need to prove that x2 + y2 + z2 ≥ 5/3.…

Q: b) = f ) then prove that x ux + y uy + z uz = 0 u

A:

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: 2. Given: XW = XY, HA I WY, KB 1 WY Prove: AHWA~AKYB. W.

A: Given that XW¯=XY¯ in ∆XWY. So, ∠XWY≅∠XYWor, ∠HWA≅∠KYBGiven that HA¯⊥WY¯, KB¯⊥WY¯So, ∠HAW≅∠KBY=90°

Q: If u=l0g Cx +ytz- 3>yz) prove that Ce+y+z) he

A: Given that u=logx3+y3+z3-3xyz Then  ∂u∂x=3x2-3yzx3+y3+z3-3xyz ∂u∂y=3y2-3xzx3+y3+z3-3xyz…

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: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

Q: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

A:

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: Selve the fallowing euler Cauchy.eg:using net hed of variation? O xy.3x y+ 6X.y-6y= Xs,in X 2. %3D

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

Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

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

A: Solution

Q: If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

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

Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

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Q: Show that for all x, y E F, there exists e with e < Emachine such that fl(x * y) = (x * y)(1+ €) is…

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

A:

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

A: