Final answer:
The statement is false because a tautology can have an ampersand as its main connective if the logical structure of the formula allows it, as seen with the tautology (P & (Q ⇔ Q)).
Step-by-step explanation:
The statement that no tautology has an ampersand as its main connective is false. A tautology in logic is a formula that is true in every possible interpretation, and the main connective of a logical formula is the connective that governs the largest components of the formula. For instance, in the tautological formula (P & Q) ⇔ (P & Q), the main connective is the material equivalence (⇔), not the ampersand. However, it is possible for a tautology to have an ampersand as its main connective if the structure of the formula permits it. For example, the formula (P & (Q ⇔ Q)) is a tautology and has the ampersand as the main connective because the part (Q ⇔ Q) is itself a tautology, and P & TRUE is equivalent to P. Therefore, the entire expression is only true if P is true, making the ampersand the main connective of this tautological expression.