3. Defining on (0,2) by 2 ~ y iff sin x = siny gives an equivalence...
Let R be the relation on N defined by xRy iff 2 divides x+y. R is an equivalence relation. You do not have to prove that R is an equivalence relation. True or False: 3 ∈ 4/R.
Determine if {(x,y) | x divides 2-y} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes Determine if {(x,y) | x and y are both even or x and y are both odd} is an equivalence relation on {1,2,3,4,5}. List the equivalence classes. Determine if {(x,y) | x and y are the same height} is an equivalence relation on all people Determine if {(x,y) | x and y have the same color hair} is an equivalence relation on all...
2. Let f : A ! B. DeÖne a relation R on A by xRy i§ f (x) = f (y). a. Prove that R is an equivalence relation on A. b. Let Ex = fy 2 A : xRyg be the equivalence class of x 2 A. DeÖne E = fEx : x 2 Ag to be the collection of all equivalence classes. Prove that the function g : A ! E deÖned by g (x) = Ex is...
Verify that the equation is an identity. sin (x-y) tan x- tany sin (x+y) tanx + tany Which of the following statements verifies that the equation is an identity? O A A tan x-tany tanx+ tany sin?(x - y) V1- cos? (x-y) 11 - cos? (x + y) sin(x - y) sin (x+y) O B. sin (x-y) sin cosy - cos x siny sin x- cos y tan x-tany sin (x+y) sin x cos y + cos x siny sin...
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the followi {{1},{2},{3},{4}} Determine whether each relation is reflexive,antisymmetric , or transitive (x,y) in R if xy>1 (x,y) in R if x > y (x,y) in R if 3 divides x + 2y
W60. Compute (sin x + cos x)(4 – 2 sin 2x – sin? 2x)e" dx sin 2x where = 6 (0,7) Mihály Be Pirkulyiev Rovsen W38. Let (an)n be a sequence, given by the recurrence: man+1 + (m - 2) an an-1 = 0 where me R is a parameter and the first two terms of (an), are fixed known real numbers. Find me R, so that lim an = 0 n-00 Tad
Find the absolute maximum and minimum values of f(x, y) = x² + 4y? – 164 – 4 on D: the set of points (x, y) that satisfy x2 + y2 < 25. Part 1: Critical Points The critical points of f are: (0,2) M Part 2: Boundary Work Along the boundary f can be expressed by the one variable function: f = f(y) = (49-y^2)+9y^2-36y-3 Σ List all the points on this side of the boundary which could potentially...
Find the exact solutions in [0,2). (1-sin(x))^2=3cos^2(x 10. Find the exact solutions in [0,27). (1 – sin(x))' = 3 cos?(x)
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.) Let Θ be a continuous random variable...
DE Homework 7 Solve the following equations by using Laplace transform: 1. " - x'- 2.= 0,x(0) = 0,2'(0) = 2. 2. " + x = sin 2t, (0) = 1, x'(0) = 2. 3. " + 3x + 25 = t,x(0) = 0,2'0) = 0. 4. " + 9. = 1, 2(0) = 0,2'(0) = 0. 5. x' + 2y' + x = 0,x'- ' + y = 0,«(0) = 0, y(0) = 1. 6. " + 2x +...