1) For the universal set U and the given sets U = {1,2,3,4,5,6,7,8,9,10}, A= {1,3,5},B = {1,2},C = {2,5}, verify that the following identities hold by calculating each side of the equation separately. a) (AUB) = A OB b) (AUB)n(AUC) = AU(BnC)

Q: Compute the component of u along v. u = (3, 2, 1), V = (1,0,1) Consider the following solution…

A: The given vectors are  and .The aim is to find the actual component of along .

Q: Let U = {1,2,3,4,5), A = {1,3,5}, B = {1,3,4), and C = {2,3,5). (a) Find A U (BUC). (b) Find (AUB)…

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Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Which numbers satisfy lal = a? Which satisfy lal = -a? What about I-al= a?

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Q: obtain 2- transform for the flow ing xCt) = tCt- 2T)

A: We have to use z transform table.

Q: 18. In each part, let T₁: R3-R² be multiplication by A, and let u,= (0, 1, 1) and u₂=(2,-1, 1) and…

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Q: 1. Write out the dual of: a. Min 3xl + 2x2 + x3 s.t. xl + x2 - x3 = 4 2x2 + x3 < 7 -xl + 3x2 2 6 х1,…

A: The given LPP is: Min 3x1+2x2+x3 Subject to x1+x2-x3=42x2+x3≤7-x1+3x2≥6x1,x2,x3≥0

Q: 13. Find the Cartesian product A x B of the sets A = {12, 9, 10} and B = {14,4}

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Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

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Q: Write down an equation of ARIMA (9,2,5) using y?

A: Given the time series process ARIMA9,2,5.

Q: Exercise 2. Let A, B C R. (a) Prove that AUB = AUB. (b) Prove that ANBCAN B. (c) Find sets A and B…

A: Solution:-

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: If u = (3,0), v = (1,2), and w = (1, –1), find a and b such that u= av + bw b = (enter numerical…

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Q: 1 5) Verify the identity CSCX-1 + = 2tanxsecx cscx+1

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Q: 1. Give an explicit formula for each S a) a, = 5a„-1 – 6a„-2 + 6(3") b) an an-1 + 6a„-2 + 3" с) а,…

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Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

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Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: Name the set identity that is used to justify each of the identities given (a) (BNC) UBNC=U (b) AU…

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Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: If u = [5,-3,-1] and = [2,-1,4] find: a) 2-u c) Find G, where F(3,-4,5) and FG = 30 b) |ū+ - 2k|…

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Q: 3. (10 points) a) Use an element proof to prove the following: for all sets A and B, A - (ANB) = A –…

A: The detailed solution is as follows below:

Q: Refer to B={ ={₁0, -6, 0.23, 3, -1.7, √7}. Determine which elements belong to the given set.…

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Q: Given u and v, find proj, u. и%3D-7, -4, -9] v = [-8, –6, 9] proj, u = %3D | Ex: 1.234 , Ex: 1.234…

A: We use the definition of Dot Product of vectors, Length of a vector, and Projection of one vector…

Q: 3) Compute A-1 using adjoint. -1 -2 -3 -41 1 2 3 Let A = 5 1 0 0

A: