1. State whether each atomic formula is true or false in @@xref

   eg-simple-model@@:

   \[\begin{gather*} \con{student}\con{anna}\\ \con{book}\con{anna}\\ \con{linguist}\con{cara}\\ \con{admire}\con{ben}\con{anna}\\ \con{admire}\con{anna}\con{ben}\\ \end{gather*}\]

2. Evaluate the following formulas in @@xref

   eg-simple-model@@.

   \[\begin{gather*} \exists x.\con{student}x\\ \forall x.\con{student}x \rightarrow \con{linguist}x\\ \exists x.\con{student}x \land \con{linguist}x\\ \forall x.\con{book}x \rightarrow \con{student}x\\ \exists x\forall y. \con{admire}y\cnct x\\ \con{student}x\\ \con{linguist}x\\ \exists x.\con{admire}x\cnct y\\ \end{gather*}\]

3. Translate the following sentences into FOL, and evaluate in @@xref

   eg-simple-model@@:

   1. Anna is a student.
   2. Ben read a book.
   3. Every student read a book.
   4. Some linguist recommended every book.
   5. No student recommended Ben.
   6. Not every student read a book.
   7. No book is read by every student.
   8. Some book is read by every student.

4. You have two predicates \(p\) and \(q\). Express the following situations in first order logic:

   1. there is no \(p\) that is not also \(q\).
   2. there is exactly one \(p\).
   3. there are exactly two \(p\)s.
   4. there is at most one \(p\).