Let X = {0, s, v}, Y = {c, d, e, i}, andZ = {0, 3, 6, 8, 9}.Let f : X → Y where ƒ f= {(o, c), (s, e), (v, d)}. Letg: Y→ Z where g = {(e, 9), (c, 8), (d, 3), (i, 6)}.g•f = {}. Let X = {q, t, u, v}, Y = {c, d, e, g, k}, andZ = {1, 2, 4, 7, 8, 9}. Let f : X → Y wheref = {(q, k), (t, d), (u, e), (v, g)}. Let g: Y→ Z whereg = {(k, 2), (d, 8), (e, 1), (g, 9), (c, 4)). Answer eachof the following questions.g ° f (q) ==g ° f(u) ==gof(v) =II

Answered: Image /qna-images/answer/e15aeb24-176d-4948-a480-059002060e99.jpg

Answered: Let X = {o, s, v}, Y = {c, d, e, i},…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Given the function f , g and h, all with source and target {1, 2, 3, 4}, defined as follows: f ={(1,2),(2,4),(3,1),(4,3)} g = {(1, 3), (2, 3), (3, 4)} h = {(1, 1), (2, 2), (3, 3), (4, 4)} 1.Which of f , g , and h are total functions, and which are partial? Evaluate 1. g(2) 2. f (f (4)) 3. g (h(4))
If u = x2 + y2 + z2 and v = xy + yz + zx and w = x+y+z between is there a relationship between,w,v find it if any.
Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)
2. Let U = {a + bx + cx2 + d³ e P3 (R) | a- 6+d3D0}, and let W = {a + bx + ca? + dx³ e P3(R)| a + 2c – d = 0}. 2(a) Find a finite subset S of P3(R) such that span S = U +W.
3) Let U={ 1, 2, 3, 4,5}, X= { 1,3,5}, Y= { 1,2,3}, and Z= 3,4,5} a. Find X U YU Z. b. Find X N Y c. Find Y N z d. Find ( XU Y) N Z e. Find X' N Y’
2. Let A = {a, b, c}, B = {x, y, z},C = {r, s, t}. Let f : A → B and g : B → C be defined by: f = {(a, x), (b, z), (c, x)}, and g = {(x, t), (y,r), (z,r)}. Find (a) Composition function gof : A→ C (b) Range of f, Range of g, Range of go f.
A = {a, b, c, d} X- {1, 2, 3, 4} The function f:A→X is defined by the arrow diagram below. Select the set of pairs that defines a function that is equal to f. O f {{a, 2), (b, 3), (c, 4), (d, 4)} Of {{a, 1), (b, 3), (c, 4), (d, 4)} Of {(a, 2), (b, 3), (c, 4), (d, 2)} Of {(a, 2), (b, 3), (d, 2)}
5. Let f(x, y) = P(X =x,Y = y), X = 2,3,4, Y = 1,2,3,4, where P is given by the table below: X = 2 X = 3 X = 4 Y = 1 Y = 2 Y = 3 1/20 2/20 1/20 2/20 1/20 3/20 1/20 2/20 2/20 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy: f,(3), fyp fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X +Y =5|Y > 1).
Q1. Let X = {m, n, p, q}, {ø, X, {p}, {m, n}, {p, q}, {m, n, p}, {q}} and Y = {a, b, c}, F = {ó,Y, {a, b}, {c}} Define f : (X, T) → (Y, F) by f (m) = a, f(n) = b, f(p) Is fa continuous function? Is f an open function? = c, f(q) = c. {ó, X, {c}, {m, n}, {a, b, c, d}, {c, m, n}}. {а, b, c, d, m, п}, т %3D {b, с, т} с X. (a) Is X a connected space? Why? (b) Is X a pathwise connected space? Justify your answer. Q2. Let X and Y = Q3. Let A = {(x, y), 4x? + 9y² < 36} C R² Is A connected? pathwise connected? Justify your answer. Q4. Let X = {m, n, p, q},T = and Y = {a, b, c, d}, F = Given the mapping f : (X,T) → (Y, F) by {d, X, {p}, {m, n}, {m,n, p}} {ø, X, {d}, {a, b}, {a, b, d}} f(m) = = a, f(n) = b, f(p) = d, f(q) = c. Is fa bijection? Is fa continuous mapping? Is f an open mapping? Is fa homeomorphism ? What you can say about the topological spaces (X,T) and (Y, F). ( Show the details of your answers). Q5. Prove that the circle {(x, y), x² + y² = 1} is not homeomorphic to the interval…
6. A.Two of the following lines are the same. Which ones? Justify your answer. I. [x,y,z] = [-2,3,1] + s [-3, 1, -2] II. [x,y,z] = [7,0,6] + t [3, - 1,2] III. [x,y,z] = [1,2,3] + p[3, -1,2] B) Either points A(-2, 1, 3), B(-3, 1, -2) and C(-1, -2, 4). Determines parametric equations of the line that passes through B and is parallel to the AC segment
a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g}, Y={a, b, c }}, and а. Z = {b, c , d, e, f} %3D a1. Find (X NY) U (YN X) a2. Find Y U (Y- X) b. Let A = {1, 2, 3} find A* A.
1. Show that y₁= ez and y2 = ze form a linearly independent set on the interval (-00,00).

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Let X = {o, s, v}, Y = {c, d, e, i}, and Z= {0, 3, 6, 8, 9}. Let f : X → Y where f = {(o, c), (s, e), (v, d)}. Let g: Y→ Z where g = {(e, 9), (c, 8), (d, 3), (i, 6)} . g • f = { }.