Question

Tommy Hilfiger celebrates casual if and only if neither Ralph Lauren nor Calvin Klein offers street chic.

Option 1: T <-> (¬R and ¬C).
Option 2: T and (¬R or ¬C).
Option 3: T or (¬R and ¬C).
Option 4: ¬T <-> (R or C)

Answer 1

The correct logical expression for the statement 'Tommy Hilfiger celebrates casual if and only if neither Ralph Lauren nor Calvin Klein offers street chic' is Option 1: T ↔ (¬R and ¬C), reflecting a biconditional relationship.

Step-by-step explanation:

The student is encountering a question involving logical statements and biconditional relationships, which falls into the category of discrete mathematics. To translate the given English statement into a logical expression correctly, we need to identify the correct logical operator that represents the 'if and only if' relationship and apply it to the proposition at hand.The main answer requires us to understand the meaning of the 'if and only if' operator, which is represented as a biconditional. According to the provided statement, 'Tommy Hilfiger celebrates casual if and only if neither Ralph Lauren nor Calvin Klein offers street chic,' the proper logical representation would require both parts of the statement to be true or false simultaneously.The correct logical expression that reflects the given statement is Option 1: T \u2194 (\u00acR and \u00acC). This expression shows a biconditional relationship (\u2194) between Tommy Hilfiger celebrating casual (T) and the conjunction of neither Ralph Lauren (\u00acR) nor Calvin Klein (\u00acC) offering street chic. The biconditional ensures that both parts of the expression must hold the same truth value for the entire statement to be true.