Question

Consider functions f : {1, 2, 3, 4} → {−1, 0,1, 2, 3, 4}.

(a) How many functions are there total? Explain your reasoning.

(b) How many functions are injective?

Explain your reasoning.

Answer #1

**Answer:**

Given data,

Consider functions f : {1, 2, 3, 4} → {−1, 0,1, 2, 3, 4}.

**(a).**

**How many functions are there total?**

Since, each element in the domain can be assigned to any of the element in the range, each element can be assigned to 6 possible elements.

And there 4 elements in the domain.

**So, 6666=6 ^{4}=1296
functions in total.**

**(b).**

**How many functions are injective?**

In injective function, each element is mapped with unique element in the range.No two distinct elements in the domain are assigned the same element.

So, for the first element 5, there are 6 possible elements to map for the second element, there are 5 possible elements and so on.

**i.e,6543=360**

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