AB,9: BC and h: CD functions.Let/:1. Show that ho (gof) = (hog) of2. If fand g are bijective, is gof3. If g of is injective, is f injective? is g injective?4. If g of is surjective, is f surjective? Is g surjective?bijective?

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Answered: AB,9: BC and h: CD functions. Let/: 1.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 12E: 12. Let and . For the given , decide whether is onto and whether it is one-to-one. Prove that your...

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26. Let and. Prove that for any subset of T of .
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions are correct. a. f(x)={ x2ifxiseven0ifxisodd b. f(x)={ 0ifxiseven2xifxisodd c. f(x)={ 2x+1ifxisevenx+12ifxisodd d. f(x)={ x2ifxisevenx32ifxisodd e. f(x)={ 3xifxiseven2xifxisodd f. f(x)={ 2x1ifxiseven2xifxisodd
12. Let and . For the given , decide whether is onto and whether it is one-to-one. Prove that your decisions are correct. a. b. c. d.

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AB,9: BC and h: CD functions. Let/: 1. Show that ho (gof) = (hog) of 2. If f and g are bijective, is gof bijective? 3. If g of is injective, is f injective? is g injective? 4. If g of is surjective, is f surjective? Is g surjective?