The new encryption protocol guarantees data security under specific conditions. If the protocol is implemented correctly and the encryption key is not compromised, unauthorized access is impossible. Furthermore, if unauthorized access occurs, it implies that the protocol was not implemented correctly or the encryption key was compromised.
Based on the statements above, which one of the following scenarios is logically impossible?
A
Step-by-Step Solution
Key idea: This is a conditional logic question. We need to translate the passage into logical formulas and find the scenario that violates the core guarantee.
Step 1: Translate the first sentence into logic.
Let = implemented correctly.
Let = key not compromised.
Let = unauthorized access occurs.
The statement is: .
Step 2: Find the contrapositive.
The contrapositive of is .
By De Morgan's laws, this is .
This perfectly matches the second sentence in the passage: "if unauthorized access occurs, it implies that the protocol was not implemented correctly or the encryption key was compromised."
Step 3: Identify the impossible scenario.
A scenario is impossible if it asserts the condition but denies the result .
In plain English: If the protocol is implemented correctly AND the key is not compromised, unauthorized access CANNOT occur.
Step 4: Evaluate the options.
Option A states: is true, is true, and is true. This directly violates . Therefore, it is logically impossible.
Options B and C state is true, but at least one of or is false. This fits the contrapositive .
Option D states is false. The original rule only guarantees when is true; it doesn't restrict what happens when is false. So being false is entirely possible.
Answer: A