If event X cannot occur unless event Y occurs first then: a) Y is necessary for X b) X is necessary for Y c) X is both necessary and sufficient for Y d) X and Y are the same event O a) Y is necessary for X O c)X is both necessary and sufficient for Y O b) X is necessary for Y O d) X and Y are the same event

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Q: 1. How many terms are there in an arithmetic sequence where a̟ = 12,an = 60 and d = 8? %3D

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

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

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A: Remark:  Direction field (slope field) is a graphical  represent of the solutions to a first-order…

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Q: Q4) Solve the boundary value problem y 3y' + 2y 0 with y'(1) = 1, y(3) = 2e* – e² h = 0.5

A: We have to solve the boundary-value problem  y''-3y'+2y=0 with y'(1)=1, y(3)=2e4 - e2

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Q: Q6: Define the Boolean ring. Is (Z,+,.) Boolean?

A: .

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A: Given: 5) a∈A 6) a,b∈A To find: Table

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Q: 1. To the right, you are given a contour plot for the function : = f(z.y). (a) Estimate the values…

A: We will use definition of partial derivative and contour diagram to  to find sign of fx and fy

Q: Q3: (A) Prove that 1. There is no simple group of order 200. 2. Every group of index 2 is normal.

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Q: Suppose we have the following sets: J = N, K = {k E Z | 0 < 2k + 1 < 20}, L = {0, 1, 2, 3, 4, 5, 6,…

A: Since we have :- J= N ={1,2,3,4,5,............} . K={1,3,5,7,9,11,13,15,17,19}.…

Q: Exercises Non-homogeneous Linear equations Solve the following equations: 5. y" - 2y' + y = 3e2x

A: The solution is given as

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A: To find parametric equations for the x- and y- coordinates of the planet P at time t.

Q: Q6: Define the Boolean ring. Is (Z,+,.) Boolean?

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Q: .... b) Let G be a group of order 2p, where p is prime number. Prove that every proper subgroup of G…

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Q: Consider the following sets: U= {set of integers) A = {3, 6, 9, 12, 15, 18} C= {3, 6, 9, 12} E=(3,…

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Q: 1 2. Expand f(2) = in a Laurent series in the region 1< |z - i| < v5. z2 + 2z

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Q: Prove logically that " C, + "C, + "C, + …· +"C, = 2".

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Q: 5. The function f(x) has a derivative g(x), shown on the graph below. (2, 1) (0, 1) 1- 1 (4,-1)…

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A: Given function is u(x,t)=sin(x)cos(t)-19sin(3x)cos(3t)+125sin(5x)cos(5t)      (1) Solution a: at x=0…

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Q: . Consider the group (Z30, +). (a) Find the orders of the elements 3, 5, 6, 7,8, 18, 19, 24 and 25.…

A: The order of an element is n , when n is the least such that, n.a=0 3.10 = 0 and 19 the least , so…

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A: To find- Use a software program or graphing utility to solve the system of linear equations. 0.1x -…

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Q: A. For each of the following arithmetic sequences, find a) the common difference; b) the equation of…

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Q: Q1: Define each of the following b) Normal group c) Nilpotent element d) Prime ideal e)Field.

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Q: 9) 9 Let I be an ideal of ring R such thut when ever R is Commutakive with identily then so is the…

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A: The figure describes a parallelogram.

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Q: Q) Consider The system -3 a) Find a fundamental matrix for thingts ten ) Find the solution o f that…

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Q: x = 2+5 cost Consider the parametric equations for 0<tsa. y = 8 sin t (a) Eliminate the parameter to…

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Q: Q4) Solve the boundary value problem y 3y' + 2y 0 with y'(1) = 1 , y(3) = 2e* – e? h = 0.5

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Q: ) Consider The system. 3. a) Find a fundamental matrn'x for thisgls tem ) Find the soluti'en o f the…

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Q: b. Calculate its tangent line at (2,0) in the projective plane and verify the result by comparing it…

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Q: 3s+2 l(s-1)(s-2)) a. 5e2t - 8et 3t+2 d. (t-1)(t-2) b. 3 sin t + 2е2t e. Зtet + 2е2t с. 8e2t - 5et

A: L-11s-a=eat.

Q: Q4: prove or disprove each of the following a) Every group has one generator. b) Every group of…

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Q: (i) Let AT = (1/2, 1/2)". Find the eigenvalues of the 2 x 2 Problem matrix AAT and the 1 x 1 matrix…

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A: We use properties of matrices.

Q: Find a principal conjunctive normal form for function f(X,Y.Z) = (X[ Y) → (¬X)¬Z), where denotes…

A: Given function,f(X,Y,Z)=(X↓Y)→¬X↓¬ZTo find: Principal conjunctive normal form for a given function

Q: 4. Find the isolates singularities of the following functions, and determine whether they are…

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