Q1/(a) Let f be a map from linear space X into linear space Y, show that whether eachone of the statements trure or flase or not.41) If A convex set of X then f(A) is a convex set of w20(2) If M is an affine subset of a space X and tEM then M-this an affine setLet R be a field of real numbers and X-M2(R) be a space of 2x2 matrices over Rthat whether there is a hyperspace of X or not.I love00

Q1/(a)1. If ( A ) is a convex set of ( X ), then ( f(A) ) is a convex set of ( Y ). I determined…

Answered: Q1/(a) Let f be a map from linear space…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 55E

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Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
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.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
26. Let and. Prove that for any subset of T of .
11. Show that defined by is not a homomorphism.
Consider the set S={[0],[2],[4],[6],[8],[10],[12],[14],[16]}18, with addition and multiplication as defined in 18. a. Is S an integral domain? If not, give a reason. b. Is S a field? If not, give a reason. [Type here][Type here]
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.
Let R, S, and T be sets. Let f: R -» S, and g: S -» T be maps. Assume we know that qf is 1-1 Must f be 1-1? Either prove that it is or find a counterexample (a) Must g be 1-1? Either prove that it is or find a counterexample (b)
Plz answer correctly asap
write in full sen
7. (10 points) Let f: A-B be onto. Prove that f(f-(C)) = C for all sets C C B.
3b

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