Predicate logic: Symbolize this categorical statement.

Question

I am a logic neophyte and simpleton studying for an exam in a graduate-level course in elementary symbolic logic. I am trying to symbolize the following categorical statement:

"No artist is a fortune teller, unless he or she reads tarot cards for someone."

Domain: people.

I symbolized the terms as follows:

$Ax = x$ is an artist, $Fx = x$ is a fortune teller, $Rxy= x$ reads tarot cards for $y$.

Here is what I got: $$(∀x)\Big((Ax∧¬(∃y)(Rxy))⟹¬Fx)\Big).$$

Is this right? Have I left something out, misplaced something, or added a superfluous bracket?

Answer 1

Looks right to me if you remove the extraneous closing parenthesis at the end. It reads "for all x, if x is an artist and there is no y for whom x reads tarot cards, then x is not a fortune teller". That's arguably equivalent to the original statement.

Answer 2

$$(∀x)\Big((Ax∧¬(∃y)(R_xy))⟹¬Fx)\Big).$$ Is this right? Have I left something out, misplaced something, or added a superfluous bracket?

Adding to Karl's answer, a human-friendlier rewrite of your suggested formalisation (minus that extraneous closing parenthesis) is just $$∀x\;\Big(Ax∧¬∃y\,Rxy⟹¬Fx\Big),$$ while logically-equivalent minimalist formalisations are $$∀x∃y\;\Big(Rxy ∨¬Ax ∨ ¬Fx\Big)$$ and $$¬∃x∀y\;\Big(¬Rxy ∧Ax ∧ Fx\Big)$$ and $$∀x∃y\;\Big(Ax ∧ Fx ⟹Rxy\Big).$$

Answer 3

This looks correct, but it can be written more simply as "if someone is an artist and a fortune teller, then they read tarrot cards for someone"

On the predicate level this can be seen in that "P implies Q" is equivalent to "not Q implies not P"