Formalize the following english statements as quantified WFF. Let S(x) be the pr

Question

Formalize the following english statements as quantified WFF.

Let S(x) be the predicate "x is a student," B(x) the predicate "x is a book," and H(x,y) the predicate "x has y, " where the universe of discourse is the universe, that is the set of all objects. Use quantifiers to express each of the following statements.



a. Every student has a book.



b. Some student does not have any book.



c. Some student has all the books.



d. Not every student has a book.



e. There is a book which every student has.

Explanation / Answer

a) (Ax) (S(x) => (Ey) (B(y) ^ H(x,y))) b) (Ex) (S(x) ^ (Ay) (B(y) => -H(x,y))) c) (Ex) (S(x) ^ (Ay) (B(y) => H(x,y))) d) - (Ax) (S(x) => (Ey) (B(y) ^ H(x,y))) e) (Ey) (B(y) ^ (Ax) (S(x) => H(x,y)))

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