(a) Prove that, if a and b are nonnegative integers such that a =4 b, then 3ª = 5 3 (b) Using (a), explain why the below defines a well-defined function f: f: Z4 Z5 f([a]4) = [39]s if a ≥ 0.

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A: The given operations are

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A: Let the function f is defined byTo sketch the graph of .To find the -values at which f is not…

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A:

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A:

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A:

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A:

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A:

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A:

Q: Prove that “if f is decreasing, then f is injective” is true. Show your work.

A: Injective function