Final answer:
In the logical statement provided, the main operator is the conditional operator represented by (⊃), which indicates that the entire expression is an implication involving other logical operations within.
Step-by-step explanation:
The student is asking about logical operators in the context of a propositional logic statement. In the given proposition, [(X ⊃ A) • (B ⊃ ¬ Y)] ⊃ [(B ∨ Y) • (A ⊃X)], the main operator is the conditional operator (⊃) that connects two larger components of the statement. The entire proposition can be seen as an implication, where the antecedent is (X ⊃ A) • (B ⊃ ¬ Y) and the consequent is (B ∨ Y) • (A ⊃X).
This is a structure used in logic, specifically in logical arguments where if the antecedent is true, the consequent must also be true, which is known as modus ponens when taken as a form of logical inference. Should there be any false component in the antecedent, the implication as a whole could still be true; however, if the antecedent is true, the consequent must be true for the entire conditional statement to be true.