1. Let X be a set and AC X a subset of X. The characteristic function XA is a function with domain X with value 1 for the elements of A and 0 otherwise, in other words: XA: X + {0, 1} So if a ¢ A l1 if a E A XA(x) = (a) For X = Z6 and A = {0, 1,5} write a table of values for XA- (b) For X = {a, b, c, d, e, f, g, h} and A = {a, e, f, 9, h}, provide reasons to show if XA bijective or not. %D %3D (c) Prove that XA(x) = 1- XA(x) for every set X and subset A.
1. Let X be a set and AC X a subset of X. The characteristic function XA is a function with domain X with value 1 for the elements of A and 0 otherwise, in other words: XA: X + {0, 1} So if a ¢ A l1 if a E A XA(x) = (a) For X = Z6 and A = {0, 1,5} write a table of values for XA- (b) For X = {a, b, c, d, e, f, g, h} and A = {a, e, f, 9, h}, provide reasons to show if XA bijective or not. %D %3D (c) Prove that XA(x) = 1- XA(x) for every set X and subset A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1.
Let X be a set and A C X a subset of X. The characteristic function YA is a function with domain X with
value 1 for the elements of A and 0 otherwise, in other words:
XA: X → {0, 1}
Jo if x 4 A
(1 if a E A
XA(x) =
(a) For X = Z6 and A = {0, 1, 5} write a table of values for XA.
(b) For X = {a, b, c, d, e, f, g, h} and A = {a, e, f, 9, h}, provide reasons to show if XA bijective or not.
(c) Prove that XA(x) = 1 - XA(x) for every set X and subset A.
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