Let C: z-3 and I – 6dz. ONone of these

Q: Let J={a: aER}, then I is Borel algebra.

A: False Statement' Detailed Explanation

Q: Let a, b, c e Z. show that ca & cb if and only if c (a, b).

A:

Q: Let 7={a: a€R}, then 9 is Borel algebra. ylgn ihi

A: True

Q: 2. Let A € M₂ (R) be given. (a) If AA¹ = 0, prove that A = On. Does this hold if A € M₁ (C)? (b)…

A: This is a problem of Linear Algebra.

Q: Let X - N(H, o). Show that the MGF of X is etu+to²

A:

Q: Let 2E An and BE Sn show that Hhen Baß'E An.

A:

Q: Let (W, t > 0) be standard BM. Show that P(n|w,1 – Wa sc) → as n → 0.

A: From the given information,  (Wt, t≥0) be standard Brownian Motion. Note: In the given situation,…

Q: 4. Let a,b,c € Z where c | (a+b). Prove that gcd(a,c) = gcd(b,c).

A:

Q: A, where OU Find det(A), adj A and A =

A:

Q: Prove that A CB P(A) C P(B).

A: We have to prove that

Q: Jin Let G beagreupsuch that I6tefs thens

A: Answer

Q: az + b If T(z) cz + d a, b, c, d e R. Show that T(RU{∞}) = RU {∞} if and only if exist

A:

Q: 9(r, t, г) — 5r(7 — сos(t)) — 82

A: We have to do partial differential here.

Q: Let w = z. In(xy?z³), then which of the following is :? O a. O b. c. O d. 0 Oe.

A:

Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

A:

Q: 13. Let T, O E L(V, W). Show that rk(T+0) ≤rk(T) +rk(o)

A: We are given that τ,σ∈L(V,W) We suppose, w∈Im(τ+σ)   ....(1) So, there exists some v∈V such that…

Q: Let a, b, c E Z. Prove that if a b and alc, then Vk EZ we have a (b+ ck).

A: ab  &  ac   Since ab, therefore b=a·m   ,  where m∈ℤ Since ac, therefore b=a·n   ,  where n∈ℤ

Q: If z1 = 1+ jb , Z2 = re¬1² , z/z2 = -10 , determine all possible values of b and r %3D

A:

Q: © If g(x, y) = In then xgx - vgw in simplified form is [c].

A: The objective is to solve partial derivative problem and explain process.

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

A:

Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

A:

Q: for AUB unih AG B inderser for is not unusual.) Then, A+B= B+ A A B= B A A (B+ C) = A B+ A C A+Ø= A…

A: In this question we need to explain about the underlined symbols ∪ ,   ∩  ,   ϕ  .

Q: Let 9={a: aER}, then T is Borel algebra.

A: Given a statement

Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: Let A, B, and C e M,(C) such that ВС - СВ %3D А"А prove that BC = CB.

A:

Q: For each subfield S of Q[i, z], determine Auts(Q[i, z]).

A:

Q: Let a, b, c E Z. show that ca & cb if and only if c (a, b).

A: Division properties are used to prove it

Q: Let a e Z. Prove that if 7 | 2a, then 7 | a.

A:

Q: Which of the following can you not use to prove A CAT S A DOG? 1. CA DO II. ZC ZD III. ZA E ZOo IV.…

A:

Q: Let w = z. In(xy² z®), then which of the following is- O a. O b. O d. O e. 0

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: Let f(r, y) = In (z³y) (1,3) = 3. then Select one: O True O False

A:

Q: let it be T=11,2,3 } S:la,b,c] Proved P(TNS)E P(S)NP(T)

A:

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: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

A:

Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

Q: 2. Let A € M, (R) be given. (a) If AA = 0, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

A:

Q: Let T, >0 be given. S

A: Given,                      Tt=KTxx, 0<x<L, t>0,                   ...(1)        T(0, t)=0,…

Q: .....………., ɑn are in A.P., where a; > 0 for all i, show that : 1 If a1, a2, a3, 1 1 n- 1 %3D Va1 +…

A:

Q: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

A:

Q: Let C: z-il-3 and I = 6. edz $ dz. Then z2 O I- 1= 4ni

A:

Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: 2. Let A € M, (R) be given. (a) If AA = 0n, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

A:

Q: Let a * b = 2ab be defined on Z*. 1. Is * Commutative? 2. Is * Associative? 3. What is the identity…

A:

Q: Let z, w e C. Show that |2 + w? + |z – w? = 2(|2|2 + |w?). %3D

A: We will show the given result.

Q: Let z, w E C. Show that |z + w[? + |z – w|? = 2(\z|² + |w|?).

A: Any complex number, Z can be represented as Z=x+iy, where x=Re(Z) , y=Im(Z) . The expression, Z can…

Q: ii) Given Z, = -1 + iv3 and Z, = -v3 + i, show that In (Z,.Z2) # InZ, + InZ2

A:

Q: 4. Let a,b,c E Z where c| (a+b). Prove that gcd(a,c) = gcd(b,c).

A:

Q: Let : fiaiy) = x@y? (12-x-y) the lon diti on Shon that C169ラ (hi2)t

A: Given that, fx,y=x3y212-x-y, x>0, and y>0. To prove, fx,y≤6912. The given function can be…

Q: Hw/O Find Adi A if A. O kind Adj A il A=

A: (1). The given matrix is:  A=521  314  463