Hi, I am struggling with the attached HW problem. Any help is appreciated. Thanks 1. (i) Let AC R. The characteristic function of the set A is defined to be XA(x) = 1 if x E A andXA(x) = 0 if x is not in A. What is X[1,2](3)?(ii) Is X[1,2] 1-1 from R to R? Why? Is it surjective? Why?(iii) Show that X[-1,0]U[1,2]| = X[-1,0] † X[1,2](iv) Does XI-1,1]U[0,4] = X[-1,1] + x[0,4]? Does X[-1,1]U[0,4] = X[-1,1] + X[0,4] – X[-1,1]n[0,4] ? Proveyour answers.

Answered: Image /qna-images/answer/6b569000-9a58-4a3e-822b-e9318e9b4285.jpg

1. (i) Let AC R. The characteristic function of the set A is defined to be Xa(x) = 1 if x € A and XA(z) = 0 if r is not in A. What is x[1,21 (3)? (ii) Is x1.21 1-1 from R to R? Why? Is it surjective? Why? (iii) Show that X[-1,0]U[1,2| = X[-1,0] † X[1,2]|

1. (i) Let AC R. The characteristic function of the set A is defined to be Xa(x) = 1 if x € A and XA(z) = 0 if r is not in A. What is x[1,21 (3)? (ii) Is x1.21 1-1 from R to R? Why? Is it surjective? Why? (iii) Show that X[-1,0]U[1,2| = X[-1,0] † X[1,2]|

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Hi,

I am struggling with the attached HW problem. Any help is appreciated. Thanks

1. (i) Let AC R. The characteristic function of the set A is defined to be XA(x) = 1 if x E A and
XA(x) = 0 if x is not in A. What is X[1,2](3)?
(ii) Is X[1,2] 1-1 from R to R? Why? Is it surjective? Why?
(iii) Show that X[-1,0]U[1,2]| = X[-1,0] † X[1,2]
(iv) Does XI-1,1]U[0,4] = X[-1,1] + x[0,4]? Does X[-1,1]U[0,4] = X[-1,1] + X[0,4] – X[-1,1]n[0,4] ? Prove
your answers.

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