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Here is another way to get the answer to the problem above. Start by just adding \(\card{A} + \card{B}\text{.}\) This is \(10 + 8 = 18\text{,}\) which would be the answer if \(\card{A \cap B} = 0\text{.}\) We see that we are off by exactly 6, which just so happens to be \(\card{A \cap B}\text{.}\) So perhaps we guess,

\begin{equation*} \card{A \cup B} = \card{A} + \card{B} - \card{A \cap B}\text{.} \end{equation*}
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