1. True or false. Justify your answer. (a) The set of integers, Z, is a subset of the set of real numbers, R. ( ) (b) Let S be a set, and let x, y € S, then x + y € S. ( ) (c) If A is the set of even integers and B = Q, the set of rational numbers, then AC B. ( ) (d) The set {(x, y) € R² | y < 0 andy > 0} is empty. ( ) (e) If A is a subset of B, and B is a subset of C, then A is a subset of C. ( )

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A: Solution :  Options (B) is correct

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A: According to rule of bartleby  we can solve only first question or three sub question of first…

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Q: - x, then answer the following (1) Find the function's domain (2) Find the function's range. (3)…

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Q: Gaussian Elimination Equations: 3X1 - 2x2 + x3 = 4 2x1 - 5x3 = 1 -3x2 + x3 = -1

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Q: Question 1 All statements below are false. Provide a counterexample of f and g each. (a) If f + g…

A: (a) Consider fx=-1x≤11x&gt;1 and gx=1x≤1-1x&gt;1 It is clear that fx and gx are not continuous at…

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A: A multivariable function is an expression involving more than one variable. If z=Fx,y, then the…

Q: (5) If f(x) =........., then f(x) is reducible in Z5[x]. (i) x³ + 2x² + 2x + 1 (ii) x² + 1 (iii) x²…

A: Solution  We know that if f(x) be a polynomial of degree upto three then if  f(a)≠0 for all a in Zp…

Q: 3. Find a vector space basis for the following field field extensions: (a) Q(√2, √2) over Q. I

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Q: 2 The tangent plane to the graph of the function ƒ : R² → R defined by f(x, y) = −1+ cos(xy) +…

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Q: Consider the following two player bi-matrix game 19 6 19 1 -10 21 A = B = 0 7 12 6 14 16 2 -9 a)…

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Q: • show that (x, y, z) = PDE : 2² + 8²4 дуг дуг + 2 x² + y² + z² = 0 824 dz² satisfies the

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Q: 1. Given the following vectors: u=(1, 2, -4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

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Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

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Q: Let S be the unit sphere with outward normal. Consider the surface Problem 4. integral [₂ (z(3² − z²…

A: Using Gauss divergence theorem

Q: (5 6 By Separation of variables, Solve the following PDES :- ²4 24 . 84² dx² 0 o u(e,t) = u(s, t) =6…

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Q: 5 By Separation of variables, Solve the following PDES- ²4 . = 4 24 dx² dt² 0 o u(e,t) = u(s, t) =6…

A: For solving the coefficients use the Fourier half interval sine series

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Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

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Q: Select the correct systems of equations. Which systems of linear equations have no solution? x+y+z=…

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Q: nding Given with their correspondin am/circuit or drawings that is related E, which is HIGHLY…

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Q: 16. Measurement Given the perimeter, P, and the lengths of two sides of the triangle, find the…

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A: To find the volume of double integral that is bounded between z=1−2y2−3x2 and xy-plane.

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Q: (1) Find three solutions to first order of the regular perturbation problem f(x)=r³3-4.001r +0.002 =…

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Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π <x<π

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Q: Let (an) be a numerical sequence such that lim |an|¹/n = 7-8 ∞ gence of the series 5a," is (A) 83…

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Q: The polar curve r (0) = 1 - 2 cos(0) is graphed for 0 ≤ 0 ≤ T. Let R be the region in the third…

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Q: show that V(x, y) = x 'f (2x+y) is the general Solution of X dv 2x dv ду = V ax

A: A partial differential equation is an equation containing more than one independent variable, one…

Q: 21 (AUC)n(BUC) 22 A-B B (((ANB)U(CNB))u(ANC))-((ANB)NC) 23

A: The union of two sets A and B , denoted by A∪B  is the set of all elements which are either in A or…

Q: Gauss - Jordan Elimination Equations: -3x + 5z -2=0 x + 2y = 1 - 4z -7y=3

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Q: Let R be a field of real number. Then Z8 is a subfield of R. To fo

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Q: Does the following series converge or diverge? Σ 4√n 10n3/2 +7n+7 n=1 The series diverges. The…

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Q: classify the following PDES :- 227 дх2 -2 822 буду +2 82 дуг =X+3y 2 2 X ох Ихх - 2ху Иху +у Иуу e

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Q: 4. Solve the following 2nd-order OPES (5 Steps) day - (d dx² + (1-1) dy Y(0) = 4 Y(0) = cas / h. A

A: Let us solve the given 2nd - order ODE using Euler method in the next steps.

Q: 3 For which values of a € R the tangent plane to the graph of f(x, y) = 1 + sin(ax + y²) at the…

A: The given graph is                                f(x,y)=1+sin(αx+y2)

Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

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Q: Q3: If f is Riemann integrable fuction, then prove the following 1) [f] is Riemann integrable 2) f²…

A: Use the properties and definition of Riemann integral to prove this as in next step.

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Q: Determine the general solution of the following differential equation: (D²-2D+1)y = 35x(3/2) ex O A.…

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Q: Given that A = (¹ 1) •[1]. and -1-eigenvector equal to 2 -1 +628968 A = has eigenvalues -1 and 3…

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