Final answer:
The question is related to logical propositions in mathematics, specifically the biconditional statement that involves an 'if and only if' scenario.
Step-by-step explanation:
The statement 'Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment' involves a logical proposition, also known as a biconditional statement. In logic and mathematics, a biconditional statement is denoted as 'p if and only if q', which means 'p' is true exactly when 'q' is true and vice versa. This can be further understood in terms of necessary and sufficient conditions, where both conditions must be met for the statement to hold.
In this context, Carnival advertising its parties (let's call this 'p') is equivalent to the implication that if Disney promotes family cruises (let's call this 'q'), then Norwegian must improve its entertainment (let's call this 'r'). Hence, 'p' is true if and only if 'q → r' is true. Moreover, this logical proposition can be symbolically represented as 'p ↔ (q → r)' where '↔' denotes 'if and only if', and '→' denotes 'implies'.