Solved: Let S be the set of all strings of 0’s and 1’s,

Chapter 7, Problem 22E

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Problem 22E

Let S be the set of all strings of 0’s and 1’s, and define D: S Z as follows: For all s S,

D ( s ) = the number of 1’s in s minus the number of 0’s in s.

a. Is D one-to-one? Prove or give a counterexample.

b. Is D onto? Prove or give a counterexample.

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