1. What is the inverse \$$f^{−1} : 3 \rightarrow A \$$ of the function \$$f\$$ given below?

2. How many distinct isomorphisms are there \$$A \rightarrow 3 \$$?

[Previous](https://forum.azimuthproject.org/discussion/2140)
[Next](https://forum.azimuthproject.org/discussion/2142)

The set \$$A := \\\{a, b, c \\\} \$$ and the set \$$\underline{3} = \\\{1, 2, 3 \\\} \$$ are isomorphic;
that is,
there exists an isomorphism \$$f : A \rightarrow \underline{3} \$$ given by \$$f(a) = 2, f(b) = 1, f(c) = 3 \$$.