4. Prove the following. a. Let a, b, c € Z with a, b = 0. Prove that if a lc and bc, and ged(a,b) =1, then abc.

Q: EXERCISE 5.7.2. Let S := {(-1)" nez}. Then Acc(S) = 10 11 (0) n. : no 013

A: This is a problem of accumulation points. Therefor it is a problem of point set topology.

Q: Given that A=( 5) and 1=). Find A in terms of A and I

A: I assume that A=(5) means that A is a 1x1 matrix with the single element 5.   To express A in terms…

Q: If A₁, A, E and P(A) = P₁, P(A)= P₂, show that P(A₁4₂)≥ 1- P₁ - P₂. (Hint: Use DeMorgan's Law (44₂)…

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Q: .Prove that A =B² = C² =I. 0 -1 Given A = B = and C = 1 0 i

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Q: 4. (а) Let a, b, c E Z. Prove that, if a | b, then ac | bc, but that the converse may be false. (b)…

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Q: Exercise 3.48. Let A,B,C,D be points such that AB = CD. Prove that {A, B} = {C,D}.

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Q: The rank and the nullity of A, respectively are 1 2 3 11 0 0 1 5 0 0 1 2 000 0 A = a. 1,3 b. 2,2 c.…

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Q: 6. Prove that if alb and k E Z, then a|(b+ ak).

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Q: Anikwenie 46. If P(A) = 0.5, P(B) = 0.40 and P(A U B) = 0.70, find P(A/B) and P(A U B) where A is…

A: Given that P(A) = 0.5 P(B) = 0.40 P(A U B) = 0.70

Q: b = Find whether {a, b} linearly independent or not. 5. Let a are

A: Given a = 20 , b = 07

Q: If a = (1, 2, 1) and b cross products. 1. a × b : = 2. b xa = = (12, 15, 1), find the following

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Q: 1 - Be X and Y variables independent with o ²X variations and o2²Y, respectively. Being Z=X+ Yand…

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Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

A:

Q: 2.4.3. Let p(r1, T2) = 16, T1 = 1, 2, 3, 4, and r2 joint pmf of X1 and X2. Show that X1 and X2 are…

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Q: Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} α1. Find…

A: Since you have given two different questions therefore we will solve the first for you. IF you want…

Q: 1. A service station has both self-service and full-service islands. On each island, there is a…

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

Q: 42. If P (A) = 0.5, P (B) = 0.40 and P (A UB) = 0.70, find P (A/B) and P(A U B) where A is the…

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Q: If u = 7 then uu? and u'u =

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Q: Let A, B, C, D be points such that AB = CD. Prove that {A, B} = {C,D}.

A: As per the question, we have to demonstrate that when the line segment AB is equal in length to the…

Q: 3. If U and V are such that u; ='x; – A, v; =y, - B, then Cov (U, V) is :

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Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: if zi = ayi for i=1,2,...,n, show that z=ay

A: Here we have given that if    then we have to show that   so here zi and yi are random variable…

Q: If X = {1,2.3}, A and B are IFSs where A= (x,{1},{2}) and B = (x,0,{2,3)) then An B

A: Intersection of Two Sets The intersection of two sets is the set of elements that are common to…

Q: Let _X=R². Find M² if M= {(a,1)}.

A: Given that, Let X=R2 Find M⊥ if M=a,1.

Q: Q.1) Evaluate IT ycos(ry) dzdy 0.

A: We will find the double integral as following.

Q: Exercise 3. Suppose that A and B are independent. Argue that A' and B' are also independent.

A: P(A⋂B)=P(A)P(B)  when A  and B are independent.

Q: ex iR Py, z)-0 fined diz H and x=2-4

A: We have to find partial derivative.

Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

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Q: Let a, b e Z where both a # 0 and b# 0. Now suppose that a = aid and b= bịd for a1, b1,d € Z. Prove…

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Q: Given that A=(2,2a,10) and B=(3x, 1,-2), if A and B are normal to each other, a is: O a. 0.25 O b.…

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Q: Let U = x'e . Find dU .

A: The given function is: U=x2eyx Therefore: dU=∂U∂xdx+∂U∂ydy

Q: The div A at p(1,1,2) for A is .... Å = x²y i + 2 x z j + 4 - z² y k - 3 ( 3 зі зј о

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Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: Q 5. If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 3, 5, 7}, B ={1, 2, 3, 5, 6, 7, 8}; werify that (AU BY…

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Q: 3. Find the value(s) of a for which ở = (-1, 2a – 1,3) and w = (2,2a + 3,–6) are parallel.

A: Two vectors  are parallel  is their cross product  is zero. So calculate  cross product  in the…

Q: Solve the initial value problem. Find the solution of the given initial value problem. Determine the…

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Q: 103 Let = 2+j"8 and z, = 4+ j06. Show that a. + =2 = =, +z2 b. 1- 2 = =-2 с. d.

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Q: (3) (i) Determine the number of positive solutions of the equation x1+x2+x3+X4 = 14, where each x;…

A: Thank you for your question!! But according to the guidelines I will be answering one question only.…

Q: 3) Let U={ 1, 2, 3, 4,5}, X= { 1,3,5}, Y= { 1,2,3}, and Z= 3,4,5} a. Find X U YU Z. b. Find X N Y c.…

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Q: Let u = (0, –2, 2), v = (1, 3, –1) and w = (2, 2, 2). If x = (0, –2, 2), then a = au + Bv + yw. O A.…

A: Given x=0, -2, 2, u=0, -2, 2, v=1, 3, -1, w=2, 2, 2 x=αu+βv+γw We will find the value of γ

Q: 1. If lul=lyl=2 and u+v+w=0, what is lwl? u, v, w are drawn below. u W

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Q: 8. If W = and V =, compute W x V.

A: To compute w*V from the given vectors.