Explain Statements of quiantifiers

Question

How would you explain these statements in terms of A(x), B(x), quantifiers, and logical connectives,

where A(x) is “x only go on big river” and B(x) is “x go on the Hudson” and Domain = Cruise ship

(a) There is a cruise ship that can only go on a big river but that doesn’t go on Hudson

(b) No cruise ship can go on big river or go on Hudson

Answer 1

(a) If you say "There is a cruise ship", we know that there is at least one cruise ship. We can use an existential quantifier (∃x). The word "but" is a conjunction (∧) between "can only go in the river" and "doesn't go on Hudson".

∃x,(A(x)∧¬B(x))

(b) If you say "No cruise ship", that's the opposite of "All cruise ship" and the word "or" is disjunction (∨). It's the same thing as "Every cruise ship cannot go on big river nor Hudson".

∀x, ¬(A(x)∨B(x))