# Let $S=\{a,b,c\}\;$ and$\;T = \{1,2,3\}$. Find $F^{-1}$ of the following functions $$F$$ from $$S$$ to $$T$$, if it exists - - $(ii)\;\; F=\{(a,2), (b,1), (c,1)\}$

Note: This is part 2 of a 2 part question, split as 2 separate questions here.

Toolbox:
• A function $g:T \to S$ if one-ne and onto is the inverse of $f:S \to T$ for every element.
• For finite sets, if $(a,b) \in f \rightarrow (b,a) \in f^{-1}$
Given $T=\{1,2,3\}, \;S=\{a,b,c\}$ and $F$ defined by $F:S \to T$ is $F=\{(a,2)(b,1),(c,1)\}$
$\Rightarrow F(b)=F(c)=1 \rightarrow F$ is not one-one.
Therefore $F$ is not invertible Therefore $F^{-1}$ does not exist
edited Mar 20, 2013