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\item \self Your little cousin needs help to plan her birthday party. There are five kids she thinks about inviting, but not all of them get along. Here is what she tells you:
My very best friend is Anthony, I have to invite him! I’m also good friends with Daisy and Connie, I want at least one of them to come. But Daisy does not like Benjamin, I can’t invite them both! But I do like Benjamin, and I also like Emily. I’d want one of them to be there, or both of them. But Emily is always fighting with Daisy, so only one of them can come.
Create a CNF from this description. You can use the following rule to make the formula shorter:\begin{align*} (\lnot s \land t) \lor (s \land \lnot t) \ent \lnot s \lor \lnot t\end{align*}
Then use the DPLL algorithm to figure out which kids your cousin should invite to her birthday party, which kids she should not invite and which kids she can invite without upsetting any other invited guests. Formulate your answer as a sentence.
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