Let A = {-1,2,-1, 12 + 1} and let B = {-1,2, 13}. a) |A U B| = %3D b) |An B| = c) |A – B| = %3D d) |B – A| =

Q: Prove that if a, bER and a < b, then |(a, b)| = |[a, b)| = |(a,b]| = b – a. %3D %3D %3D

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Q: Exercise 2. Show that if B + Ø then dom(A × B) = A. %3D

A:

Q: Exercise 4.7 Consider n observations for which y = a + bxi, b>0, holds. Show that = 1

A: Given that there are n observations. yi=a+bxi

Q: Prove that if a, b e Z – {0}, then gcd(a, b) = gcd(a, -b)

A: Solution:-   gcd a,b= Greatest common divisor of  a  and  b ∗Every integer  that divides  a  and  b…

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

A:

Q: Show that if a\b and gcd(b, c) = 1 Then gcd(a,c) = 1 %3D

A:

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: Show that if A ⊂ B, then C – B ⊂ C – A.

A:

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

A:

Q: In Exercise 22, let u = PQ\ and v = PR\ , and find (a) the component forms of u and v, (b) u ∙ v,…

A: a) Answer(a): u=(-2,6,-2) and v=(3,6,-3)

Q: 2. Show that cÃ=cA.

A:

Q: In ([0, о), т оос), if A %3DN, then A'%- Оа. А-{1} O b. [0,0) О с. (0, о) O d. Ø О е. А

A: ( [0, infinity) , Tcoc)  Since it is Co-countable topology. All countable sets are closed in given…

Q: Exercise 2.5 Prove that if m" (AAB) = 0, then m* (A) = m* (B). Hint Note that AC BU(AAB).

A:

Q: 4. Write a flow proof, Use the information from the diagram to prove that A ABD A CDB. A ....

A: Given:

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: Let X ∼ Bin(n, p), and let Y = n − X. Show that Y ∼ Bin(n, 1 − p).

A: Here X follows Binomial with parameters n and p. Here, Y=n-X. Then Y takes the values n-0, n-1,…

Q: Show that A is skew symmetric if and only if ai j = −aji for all i, j.

A: Suppose A be any square matrix of order n such that A=a11a12⋯⋯a1na21a22⋯⋯a2n⋯⋯⋯⋯⋯an1an2⋯⋯ann First,…

Q: Prove that ∀a, b, k ∈ Z that ((4|k) ∧ (k = ab)) ⇒ (2|a ∨ 2|b)

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Q: Prove that if A is skew symmetric and nonsingular, then A−1 is skew symmetric.

A: Given that A is skew symmetric. It means AT=-A  We have to prove that A-1T=-A-1

Q: Let A,BE Mmna Shaw that vTAw= V' Bw for all VER™ end WEIR" if and only if LA=B. %3D

A:

Q: Prove that, if (a%m)=(b%m) then m| (a-b)

A:

Q: 48. Let A, = {...,-2, –1,0, 1, ...,i). Find %3D a) Aj. b)4-

A: The meaning of the set  ∪i=1n Si where S1,S2,……,Sn are the sets . The set ∪i=1n Si is collection of…

Q: A survey of farmers showed that of the farmers, 126 grew only wheat, 111 grew only corn, 93 grew…

A:

Q: Suppose that A= {a,b,c,d} Then |A| =.?

A: Let X be a set , then X be number of elements in set X

Q: Show that if A is nonsingular and AB = O for an n × nmatrix B , then B = O .

A: We have given  matrix A is non singular and AB=0 for an n×n matrix  B. We have to prove that B=O

Q: Prove that if r>3 and y > 4, then ry > 11.

A:

Q: If A = 2x²,-3yz, xz² and qp = 2z - x³y. Evaluate A Vop and A x Vp at the point (1, -1, 1).

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Q: Let A, BCR x R defined by A= {{n,m)|n, m € N, 0 < 2m(n + 1) – 3 < 5}, and B = {(1,1), (1,2), (2, 1),…

A:

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

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

A:

Q: If A and B is a symmeyric, proof that AB-BA is a skew symmetric?

A: We know that a symmetric matrix is a square matrix that is equal to its transpose and a…

Q: Show that for n, m e Z+, gcd(2" – 1,2m – 1) = 2gcd(n,m) – 1.

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: Show that if a \ b and gcd(b, c) =1 Then gcd(a,c) = 1

A:

Q: Prove that, if m | (a-b) then (a % m) = (b % m)

A: Since you have asked multiple questions we will solve the first question for you. If you want to be…

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: True or False   Consider the following model, Yi = β0 + β1Xi + ui,E[ui|Xi] = 0,i = 1,...,n…

A: Solution: As per the guidelines first three parts should be answered.

Q: If A and B are n × n and A + B is symmetric, then A and B are symmetric.  True or False...provide a…

A: If A and B are n × n and A + B is symmetric, then A and B are symmetric.

Q: es of the matr

A:

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: Exercise 2 Given KB = (X→Y) ^ (Y→Z), and a = (X→Z) Is KB |= a is valid or not?

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

Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

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Q: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

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Q: Let F1 and F2 be 4-dimensional flats in R6, and suppose that F, N F, # Ø. What are the possible…

A:

Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)

Q: 2. If (x, y) is a sa

A: As per the guidelines, we are supposed to solve one question. Kindly repost the other question as a…

Q: If A = {1,2,5,8, 9} and R = {(x, y) E A X A 3 x + 1 = y}, S = {(x, y) E A X A 3 y +1 = x} %3D %3D…

A: SOLUTION-

Q: (c) If gcd(a , 133) = gcd(b , 133) = 1, show that 133|al8 b18 %3D %3D

A: