Consider sets A and B as follows: A = {x € Zx = 8k + 28 for some k E Z} %3D %3D {y € Z[y = 4m for some m e Z} %3D %3D i) Is A C B? If so, prove this proposition. If not, prove A EB. ii) Is BC A? If so, prove this proposition. If not, prove BEA. iii) Is A = B? Explain why or why not. %3D

Q: Given the following information, determine the value of x: u = [2x, 5], v = [3x, 1 and += 7x.

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Q: W = U. W = 5, and ||W||2 a, then the value of a is: If U =

A: Given, U=12, W=xy U·W=5 and W≥α.

Q: If ||V|| = 5, ||W|| = 6 and -a < V ·W < a, then the value of a is equal to: О а. 30 O b. 10 О с. -30…

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Q: Let X is p.d.f,f (x) = k(2 - x) 0 <x < 2, then the constant k = ..... A) 1 B) C)를 D) 2

A: We have given that,  X be the random variable having probability density function f(x) = k(2 - x),…

Q: Let a, b E P and let s,t E Z. Suppose that sa + tb = 10. Then is it possible that (a,b) = 20? (Give…

A: Given problem:- Let a, b ∈ P and let s,t ∈ Z. Suppose that sa + tb = 10 Then is it possible that…

Q: 5- If 2 - 3 3 -1 = | In y 1 5e? -5 -2 + 5 2 4 3 1 5 8 Then, what is the value of x+y+z=?

A: 5)

Q: 2.6.10. Take X = R, and find E°, DE, and E for each of the following sets. (a) E %=D {1, 글, 흙, }.…

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Q: given A={x I x2 - 1 = 0 }, B = {x I x2 + x - 2 = 0}, and C = {x I x3-x2=0} A, B, C Ⅽ R a. A U ( B ∩…

A: A=x:x2-1=0B=x:x2+x-2=0C=x:x3-x2=0 Then we have to evaluate A∪B∩C.

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: arc • If X₁ Y dos connected, then so is XxY.

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Q: 2) prone À . § = A, Bx +Ay By + Az Bz %3D

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Q: Prove that if AT A = A, then A is symmetric and A = A².

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Q: Which of the following statements are true? I: If F, and F, are 5-dimensional flats in R', then the…

A: Given that F1 and F2 are 5- dimensional flats in R7.

Q: f G = Zs and G2 = Z, then G = G, G2 is Cyclic a) True b) False C) None of the abo

A: We have to choose the correct answer from the given option according to the given condition…

Q: z2-sinz The residue of f(z) = } at z = 0 equals z2 а. —1 2 O b. -1 О с. 1 d. 7

A: We have find residue at z=0 and given double integration.

Q: 5.). Trueor Falseg b. II true igihe a counter example. an Pfemple. If Foalse, gire b.) A t CB O <(A…

A: Given: The expression is A×B-C=A×B-A×C.

Q: Given that A and B are independent with P(A ∪ B) = 0.8 and P(B c ) = 0.3, find P(A).

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Q: Let A, B, and C be sets. (a) Find |(A U C) \ B|provided |A| = 50, |B| = 45, |C| = 40,|A N B| = 20,…

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Q: Activity 1. below each number) into its proper column and row. Complete each proof by placing each…

A: We have to complete the given table of statements and reason using the hints given below.

Q: Let and 001 1 0 0 2 1 A = 0 If the entries of A and v belong to Z3, what is the third entry of Av? 2…

A: Recall matrix multiplication and modulo arithmetic.

Q: Let G = Z¬ÐU(5). The identity of G is O 7 O 28 35 O 12 O 5

A: We know that U(5) is isomorphic to Z4.

Q: Question 7: Suppose that K,H ≤ G such that G = HK and Hn and hk = kh, VhEH and kE K. Show that G≈ H

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Q: Is the set S= {I E R² | e21+2=2 >1} convex? %3D

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Q: 3. Show by an example that the following statements are false. i. a - (b c) = (a - b) (a - c) for…

A: ( i )  a - (b • c) = ( a - b ) • (a - c )  fo all a , b , c belongs to real number R   We show that…

Q: Find f, and f, and evaluate each at the given point. 7xy f(x, y) = (1, 1) 2x2 + 2y2" 5,X, v) %3D .…

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Q: Show that if (, y, z) is a Pythagorean triple then 60|xyz.

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: 2. 2. 2. 2. is it Linear tsenstormetion? Li L (U+v). LLu) +L(V). LkU). k L (U).

A:

Q: ✔Question 12 A C D to A at peint D, which statement must be true? Select all that apply. m.BDE =…

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Q: a-x a- y = qy px YZ prove that x, y, z are in H.P. If a-z and p, q, and r are in A.P., then If a, b,…

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Q: If Z,=1+2i , find the Set of values of Z for which 1) f Z Of Zz %3D %3D

A: Given z1 = 1+2i Let z2 = x+yi (i) We want |z1 + z2| = |z1| + |z2| We have: Thus According to the…

Q: QUESTION 7 For all sets A and B, (AXB)n(B×A) = Ø. O O False True

A: Given SET A and B

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: Question 9. Let A E Mn,n. Prove that A is symmetric if and only if Ax · y = A"x · y for all x, y E…

A: See the solution it is done step by step.