(b) Show the following.Two mappings f:X→ Y and g:X→ Y are said to be equal (and wewrite this f = g) if f(x) = g(x) for every x in X. Let f, g, and hbe any three mappings of a non-empty set X into itself, and showthat multiplication of mappings is associative in the sense thatf(gh) = (fg)h.

I am going to solve the problem by using some simple calculus to get the required result of the…

Answered: (b) Show the following. Two mappings…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

{T E Sn | sign(T) = 1} has elements for all n > 2. Show this by (b) Prove that the set An := constructing a suitable bijective mapping between An and Sn \ An . Remark: Without justification, you may use the fact that if there is a bijective mapping between two (finite) sets, then these must have the same number of elements.
how would you prove this
1. Let A = {1,2,3}, B = B = {4,5,6}, The functions f : A → C and g: B → C are defined by f(1) = 7, f(2)= 9, f(3) = 7, Does there exist a function h: A → B such that go h = f? Does there exist a function k : B → A such that fo k = g? Justify your answers. {4,5,6}, C = {7, 8, 9, 10}. g(4) = 10, g(5) = 7, g(6) = 9.
i need complete solution step by step
Determine whether the following sets form sub- spaces of R³: (a) {(x1,X2, X3)" | x1 + x3 = 1} (b) {(x1, x2, X3)" | x1 = x2 = x3} (c) {(x1, X2, X3)" | X3 = x1 + x2} (d) {(x1, X2, X3)" | X3 = x1 or x3 = X2}
15. Let f: A → B and g: C → D. Define fx g = {(a, c), (b, d): (a, b) = f and (c,d) = g}. (a) Prove that f × g is a mapping from A × C to B x D. (b) For (a, c) = A x C, write (f× g)(a, c) in terms of f(a) and g(c).
Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3, then (p1, p2) in S (or p1 ~ p2) if (x1 - x2) + 2(y1 - y2) + 3(z1 - z2) = 0. Describe all equivalence classes. [Continuation of an earlier question.]
Let A be a non-empty set and f.g:A→A be any functions such that fOq is the identity map of A. Then * g is one-to-one None of these O g is not necessary one-to-one O f and g are the identity maps g is the identity map but f is not necessarily the identity map
Let R be a relation and S its reverse. Show that R is injective if and only if S is well defined, and that R is surjective if and only if S is everywhere defined.
(b) Define the cartesian product X x Y of two sets X and Y, and the power set P(X) of X. Find X × Y and P(X) for X = {x, y, z) and Y = {(1,2), 3}.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

(b) Show the following. Two mappings f:X→ Y and g:X→ Y are said to be equal (and we write this f = g) if f(x) = g(x) for every x in X. Let f, g, and h be any three mappings of a non-empty set X into itself, and show that multiplication of mappings is associative in the sense that f(gh) = (fg)h.