Let X={1,2,3}.  Let P(X) be the set of all subsets of X (i.e. Power set of  X). Let R be a relation defined on P(X) by the following. For all sets A and B in P(X)P(X), ARB iff |A|=|B||A|=|B|.  Is R an equivalence relation?

Q: Use induction to prove: 7 - 1 is divisible by 6 for each integer n ≥ 0.

A:

Q: 1) Let f(x) = 1 + 2x³ - x and g(x) = 2x + b, for xeR, where b is a constant. a) Find (gof)(x). b)…

A:

Q: 3x.-+ ㅎ 1 X ₁²+² - x = 0 50 - 2x₁ - x₂ = 0 - - 20 = 0

A: 32x1-12-2λ=0               i12x2-12-λ=0                  ii50-2x1-x2=0              iii

Q: ► Exercise 11.2. Prove Proposition (c) A finite product of covering maps is a covering map.

A:

Q: (a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z²k through…

A: Given, F→(x,y,z) = z2k→The surface is the upper hemisphere of  x2+y2+z2=25.

Q: a) Integrate the function f(x, y, z)= yz over the part of the sphere x² + y² + z² = 4 that lies…

A: The given problem is to integrate the function f(x,y,z)=yz over the part of the sphere x2+y2+z2=4…

Q: Use modified Euler method to solve dy dt =-2y+4 e dx yx dt 33 3 Over the range of t= [0 0.6], using…

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

Q: Suppose that license plates in a certain municipality come in two forms: (1) four letters (A... Z)…

A: Answer :- Four letters (A...Z) followed by two digits(0...9)  As each letter has 26 chances and each…

Q: Let z=6. Differentiate the function f(x) = 7x7 - 8x + z. The required derivative is f '(x) =

A: Please find attachment

Q: Give an example of each of the following or prove that such a request is impossible. infinite family…

A: To give an example or prove such request is impossible of infinite family of open sets S1⊇S2⊇...…

Q: A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field…

A:

Q: Determine whether the function f: ZxZ → Z is onto if a) f(m, n) = m+n. b) f(m, n) = m² +n². c) f(m,…

A: We know that a function f:X→Y is said to be onto if every element of set Y has a preimage in set X.…

Q: 5. Given a small cube resting on the xy plane with corners at (0, 0, 0), (a, 0, 0), (a, a, 0), and…

A: Let given points are  A0,0,0,   Ba,0,0 ,   C(a,a,0),  D(0,a,0)         From gauss divergence…

Q: You owe $2300 on a credit card with 21% APR if you want to pay it off in 18 months, how much would…

A: Loan amortization formula is  A=Pi1+in1+in-1 Where A is periodic payment amount, P is loan amount,…

Q: Consider the following region R and the vector field F. a. Compute the two-dimensional curt of the…

A:

Q: Solve the system of linear equations using matrices. 6x - y -28 - 5z 4x + 2y = 10 5x + 6z = -23…

A:

Q: nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of…

A:

Q: Suppose that surface o is parameterized by r(u, v) = (u cos (2v), u sin(2v), v), 0≤u≤ 5 and 0 ≤u< ¹T…

A:

Q: ƒ : R → Z via f(x) = x²-10 5

A: The given function f:ℝ→ℤ such that fx=x2-105. We have to check whether the function is one-to-one or…

Q: use the laplace transform to solve the initial value problem X X = 1 + tet initial condition: y (0)…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Let x be non zero. Find the derivative of the function x cos( 3 + 4 π). The required derivative is…

A:

Q: 1. Consider the curve in parametric form x (t) = t³ - 3t y(t) = 3t²-9 a) Find the point(s) where the…

A: Slope of tangent line to any curve dydx For any parametric curve x(t) , y(t) dydx=dydtdxdt Note :…

Q: A truck traveling at 44 ft/sec decelerates at a constant 2 feet per second squared. How many feet…

A: Initial velocity =44 ft/ second Deceleration with constant speed of 2 feet/sec2

Q: Use the crossing-graphs method to solve the given equation. (Round your answer to two decimal…

A:

Q: [Proof] Prove that the congruence (x² − 2)(x² – 19) (x² - 38) = 0 (mod p) has a solution for every…

A:

Q: Consider the following 3 x 4 matrix A and its Reduced Row Echelon form, denoted U. [10-4 1] [120 1]…

A: The two given matrices are A=120101201201, U=10-4101200000 1. To find a basis and dimension for the…

Q: Consider the Boundary-Initial Value problem Jºu 25 Ər² u(0, t) = 0, u(3,t) = 0, t>0 du u(x,0) = x(3…

A: The given problem is to find the solution for the given boundary value problem with given initial…

Q: y" + (x-7)y = 0

A: To find the series solution of the given differential equation. We consider a series solution in…

Q: Consider the curve C: y=cos x. You may assume that for all values of x = [0,1/2] the curve C lies on…

A: given y=cosx and 1-2xπ≤cosx≤-x2+4+π42 integrating both sides , we get ∫0π21-2xπdx≤∫0π2cosx…

Q: You are part of a team to go on a geological dig site and will arrive at the airport shown in the…

A: From the figure, it is given that AB=28 mi, AD=40 mi, DC=30 mi, ∠BAD=25°, ∠CAD=47° and ∠ACD=77°. The…

Q: quation, Use the power series method to find the solution, y = y(x), to the differential d²y dy -…

A:

Q: Use Green's Theorem to evaluate the line integral of F = = (x³,9x) around the boundary of the…

A:

Q: > Evaluate [ ²(x² + y²) dx + (x + y)²dy C › C is the triangle with vertices (1,1), (2,2) and (1,3)

A:

Q: Find the solution of the Differential Equation (D³ - 3D²+4) y = 40cos2x+6

A: D3-3D2+4y=40cos2x+6

Q: 3. (Section 17.6, 17.8) Consider S₁x² + y² = 9, S₂: z=0, (a) Graph surface S. = xî + yĵ+ (2² − 1)k.…

A: The given function is F=xi^+yj^+z2-1k^, and the Surface S is bounded by the surfaces S1:=x2+y2=9,…

Q: Solve the linear programming problem Minimize C=7x+By Subject to 4x*7y > 28 What is the minimum…

A: Given linear programming problem is

Q: The function f(x) = ln(1-x2) is represented as a power series f(x) = ao cnxn. Find the FOLLOWING…

A:

Q: 4. Solve the two-point boundary-value problem Jy" + 2y' + 10x = 0, [y(0) = 1, y(1)=2 for y() and y()…

A: Given : The equations  y'' + 2y' + 10x = 0,y0 = 1,    y1 = 2   To solve : The two-point…

Q: 24. Show that Leªth} (s) = n!/(sa)"+¹ in two ways: (a) Use the translation property for F(s). (b)…

A:

Q: Use the divergence theorem to write a triple integral that is equivalent to the flux integral - = 64…

A:

Q: Sketch the image of A JKL under the similarity transformation composed of a size transformation…

A:

Q: find the laplace trans form of the function, F(t) = et cos ht

A:

Q: Find the equation of the parabola by using three points (4,0), (2,8), and (6,0). Step 1. Write the…

A:

Q: Suppose that y varies directly as the square root of x, and that y = 30 when x = 100. What is y when…

A:

Q: Last year OHaganBooks.com experimented with an online subscriber service, Red On Line (ROL), for its…

A:

Q: 4. 3t²¹ - 2² +1 +4 314

A: Given that f(t)=3t4-2t2+1 Laplace Transform A function is said to be a piecewise continuous function…

Q: find the complete solution of the DE y''-2y' + y = e^x/x using MVP.

A:

Q: s2

A:

Q: A positive integer N is said to be a congruent number if it is the area of a right triangle with…

A: