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4. (a) (1 point) Translate the following sentence into a predicate formula: There is a student who has e-mailed at most n other people in the class, besides possibly himself. The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are • equality, and • E(x, y), meaning that "x has sent email to y". (b) (2 points) Explain how you would use your predicate formula(or some variant of it) to express the following two sentences. . There is a student who has emailed at least n other people in the class, besides possibly himself. . There is a student who has emailed exactly n other people in the class, besides possibly himself.

4. (a) (1 point) Translate the following sentence into a predicate formula: There is a student who has e-mailed at most $n$ other people in the class, besides possibly himself. The domain of discourse should be the set of students in the class; in addition, the only predicates that you may use are - equality; and - $E(x,y)$, meaning that "x has sent email to $y_{′′}$. (b) (2 points) Explain how you would use your predicate formula(or some variant of it) to express the following two sentences. - There is a student who has emalled at least $n$ other people in the class, besides possibly himself. - There is a student who has emailed exactly $n$ other people in the class, besides passibly himself.

(a) The predicate formula for the given sentence can be expressed as: ∃x (Student(x) ∧ (∃y1...∃yn (...

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