Exercise 13.

Consider functions \(f: \{1,2,3,4\} \to \{1,2,3,4,5,6\}\text{.}\)

  1. How many functions are there total?

  2. How many functions are injective?

  3. How many of the injective functions are increasing? To be increasing means that if \(a \lt b\) then \(f(a) \lt f(b)\text{,}\) or in other words, the outputs get larger as the inputs get larger.

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