# Math Help - Set Theory

1. ## Set Theory

Let X and Y be finite non-empty sets. Write down a formula for the number of different functions from X to Y.

Ans: #Y^#X. (hash symbol doesn't seem to work in latex..?)

Can anyone explain why this is?

2. If n is the number of elements in X and m is the number of elements in Y for each $x \in X$ we have $m$ choices in $Y$ for its image in a mapping. Therefore we have $m^n$ possible mappings.

3. I need an example to picture this. What are the 8 possible mappings then in X has 3 elements and Y has 2?

4. Suppose X = {a, b, c} and Y = {d, e}.

1. f: X->Y

f(a) = d
f(b) = d
f(c) = d

2. f: X->Y

f(a) = d
f(b) = d
f(c) = e

3. f: X->Y

f(a) = d
f(b) = e
f(c) = d

4. f: X->Y

f(a) = e
f(b) = d
f(c) = d

5. f: X->Y

f(a) = e
f(b) = e
f(c) = d

6. f: X->Y

f(a) = e
f(b) = d
f(c) = e

7. f: X->Y

f(a) = d
f(b) = e
f(c) = e

8. f: X->Y

f(a) = e
f(b) = e
f(c) = e