Consider functions f: {1,2,3} → {1, 2, 3, 4, 5, 6, 7}. a. How many functions are there total? b. How many functions are injective? c. How many of the injective functions are increasing? To be increasing means that if a < b then f(a) < f(b), or in other words, the outputs get larger as the inputs get larger.

Q: d) Is the composition of two one-one functions a one-to-one function? e) Is it true that P(A) ≤ A?

A: For part (d), the answer is YES.

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Q: How

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