Let S be the set of all strings in a's and b's, and define C: S → S by C(s) = as, for each s ∈ S. (C is called concatenation by a on the left.) (b) Show that C is not onto. Counterexample: The string _____ is in S but is not equal to C(s) for any string s because every string in the range of C starts with _____.
Let S be the set of all strings in a's and b's, and define C: S → S by C(s) = as, for each s ∈ S. (C is called concatenation by a on the left.) (b) Show that C is not onto. Counterexample: The string _____ is in S but is not equal to C(s) for any string s because every string in the range of C starts with _____.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.2: Integral Domains And Fields
Problem 7E: [Type here]
7. Let be the set of all ordered pairs of integers and . Equality, addition, and...
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Let S be the set of all strings in a's and b's, and define C: S → S by
C(s) = as, for each s ∈ S.
(C is called concatenation by a on the left.)
(b) Show that C is not onto.
Counterexample: The string _____ is in S but is not equal to C(s) for any string s because every string in the range of C starts with _____.
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