can anybody critique, and if necessary, correct, my reasoning in the following translation?
c. Either Alice has a dog and Carol has a cat, or Bob has a dog and Carol does not have a cat.
This is two compound conjunctive statements connected by an “or.” So, the main logical operator is “or,” which is symbolized as “∨.” This statement as a whole is a compound disjunctive statement. It is not an inclusive disjunctive because it cannot be the case that Carol both has and does not have a cat; it cannot be the case, for example, that Alice can have a dog in the case that Carol does not have a dog, so whether Alice or Bob are dog owners is wholly contingent upon whether or not Carol has a cat.
On the left side, we have two atomic statements. The first says that “Alice has a dog” and is symbolized by A. The second atomic statement says that Carol has a cat, which is symbolized by C. These two left hand atomic statements, when read in conjunction, are symbolized as (A ∧ B).
On the right side, we similarly have two atomic statements that work in conjunction to form one compound statement: “Bob has a dog and Carol does not have a cat.” This is symbolized as (B ∧ C).
Since we have outlined how the different components of the statements are symbolized, when we add them all together as a whole, we have (A ∧ B) ∨ (B ∧ C).
Note: It is possible that both Alice and Bob have dogs, respectively, i.e., “Alice has a dog, Bob has a dog, and Carol has a cat,” or “Bob has a dog and Alice has a dog, but alice does not have a cat.” Thus the reason that this disjunctive compound statement as a whole is non-inclusive is wholly contigent upon Carol’s cat ownership status.