Predicate Logic with Nobody

Question

Nobody is a college student and not smart. How does this translate into predicate logic? I am stuck between two:

¬∃x[person’(x) ∧ student’(x) ∧ ¬smart’(x)]

¬∃x[[person’(x) ∧ student’(x)] → ¬smart’(x)]

Thanks!

Where did ambitious come from? It is not in the statement you are translating... — Mark Fischler, Nov 18 '19 at 23:10
Sorry! I was saying something else when typing, but what if it was a word like smart instead? Am I close? — joseyjones, Nov 18 '19 at 23:12

score 2 · Answer 1 · answered Nov 18 '19 at 23:16

2

The first translation is the accurate one of the original English statement.

The second "translation" is actually false (even assuming the English statement is true): consider an $x$ that is not a person, or an $x$ who is not a student, or an $x$ who is a smart student—all of these are examples showing that the negated-existential is false.

answered Nov 18 '19 at 23:16

Greg Martin

78,820

This makes sense! Thank you! – joseyjones Nov 18 '19 at 23:37

Predicate Logic with Nobody

1 Answers1