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In general, there is no relationship between \(\card{B}\) and \(\card{f\inv(B)}\text{.}\) This is because \(B\) might contain elements that are not in the range of \(f\text{,}\) so we might even have \(f\inv(B) = \emptyset\text{.}\) On the other hand, there might be lots of elements from the domain that all get sent to a few elements in \(B\text{,}\) making \(f\inv(B)\) larger than \(B\text{.}\)

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