I am supposed to transform the following sentence into predicate logic: "At most two men can be accepted to each position in Google" Predicates are already given:
J(x, y) - x is a job position in company y
A(x, y) - x is accepted to job position y
My logic so far is the following: $∀x∀y∀u∀z (x ≠ u ∧ y ≠ u ∧ x ≠ y) ∧ (J(z, Google)∧ ...))$
Instead of the ... I thought about writing many cases with OR's in between (x and y got accepted to job z and NOT u was accepted to job z OR not x,y, and u were accepted to job z, etc.)
I believe there is a better way to do this than to write literally every case like this to show that at most 2 men can be accepted to each position