4. Let E = {4, 5, 7} and F = {5,7,8}. The following statement is true. Justify it. %3D %3D Vy E E[y is prime →3z E F(y + z is divisible by 5)]

Q: Let u = PQ and v = PR. P = (2, -1, 3), Q = (0, 2, 1), R = (6, 2, –1) %3D (a) Find the component…

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Q: 3 Let x = -4. Then, a. ||x||2 = -4 O b. ||æ||2 = V26 Oc. |l리2-0 O d. ||2||2 = 3 e. ||r||2 = 4 O f.…

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Q: Each diagram shows rectangle ABCD. Draw the image under each transformation. 5. Atranslation of 3…

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Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: Two students are named to present their work from a class of 12 students: 3 from electrical…

A: Total = 12 students  Number of electrical = 3 Number of tele com= 5 Number of computer = 4 X: Number…

Q: Let f (x) = 2:c – 7 and 9 (x) = 4.x + 3_Find (g o f)(3). %3D -1 55 7 49

A: Given f(x) = 2x - 7 and g(x) = -4x+ 3 We need to find (g o f)(3). The solution is given below.

Q: et z = r²y – ry², I = e *,y= e*, then which of the following is O a. 2et + 2e 2t O b. 0 OG -2e4 – 2e…

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Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

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Q: 15. Find x so that m || n. (5x – 20)°

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Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: Consider Check all that apply. OA. first order B. ODE C. PDE OD. linear O E. third order OF second…

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Q: 2. Let f: ZxZ-ZxZ be defined by f(m, n) = (3m+n,n²) a. Is fone-to-one? b. Is fonto?

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Q: Let a b. A = d Lg h i Find a. det(3A) b. det ((2A¬)) P Type here to search %23

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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: [1 2 3] If Ax = b where A = 1 1 2, find x if Lo 1 2.

A: Using matrix notation a system of equations can be expressed in the form Ax=B. In this problem the…

Q: If f(x) = then, %3D 1. D; = R R; = {1,0} 2. D, = [1,00) R; = [0, c0) 3. D; = R R; = {1,–1} 4. D; =…

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Q: х Pr Product .3 2 a .4 .4 2 7 h

A: Consider the given table, X Pr Product=X×Pr 0 .3 0 2 a .4 5 .4 2 7 b c

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A: Evaluation of the indefinite integral, by using substitution method

Q: 1. D, [3x²y+In(xy²)] За + In(xg In(xy³)]

A: Given,

Q: 3. Prove that if a E Z then the only positive divisor of both a and a + 1 is 1.

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Q: Which of the following statements is always true (select all that apply)? Р (AUB) — P(A) + Р (В) Р…

A: The probability of an event is the chance of occurrence of that event.

Q: 25. Let A = If g(x) = x² – 25. Find all numbers i for which A is a root of the polynomials. A. -5…

A: "According to the guidelines of Bartleby. solve only question 25". Given: A=520k and gx=x2-25. The…

Q: 8 12 -4 -2 -5 12R 5R 11R 6R 3R 9R P(X=x) Evaluate R OA. 47 Ов. 1/46 OC. 1/40 OD. 40 OE. None of…

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Q: Compute e-1/z ₁-3+1° -dz, and $ e¹/2² |z-i|=3/2 2² +1 dz.

A: Concept Used If a complex function f(z) is analytic within and on a closed contour c inside a…

Q: find all fau Secmd order factial desirathives. Icoslbxtc)

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Q: 3. Let n E Z. Give a direct proof that there exist x, y E Z such that n = 55x + 78y.

A: Objective : To prove for any n∈ℤ ∃x,y∈ℤ such that n=55x+78y Prove for n=1, Greatest common divisor…

Q: 1. Now we are going to list all the cosets of H in G. (a) Let G = S4 and let H = D4. How many cosets…

A: The complete solutions are given below

Q: 2. Let G = Z,xZ4, and find [G:H] for: a) H = {0}xZ4. %3D

A: We have to find [G:H]

Q: (a) Find the left cosets of {e, (1, 2)} in S3. (b) Find the right cosets of {e, (1, 2)} in S3.

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Q: Suppose A E C such that X(2+i, 3 – i) = (5- i, 7- 5i). Then (1) A = (1– i) (2) A = (2– i) (3) Does…

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Q: 15) Find SR 16) Find VW E R %23 -2x – 6 M %3 W N %23 2x – 14 x + 15 x+ 2 x+ 21 F V.

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

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

A: We have to solve given initial value problem using the Laplace transform method

Q: -) Given Xn+1 = X +2X + 3Xn, shown below (also shown is Xn+1 = X„), and X5 = 0.1, %3D %3D %3D what…

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Q: Pearson’s r(50) = .75, p = .03 can be interpreted as: Group of answer choices X and Y have a…

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Q: The LCD of, and is 6xy. 3. 2x21 6y' 3xy O True O False

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