Question

Neither the Sami nor the Kephrian delegations attended the international conference. Beforehand, the delegations of Daqua and Kephria, allies whose governments had grievances against Tessia, officially announced that one or both of the two would stay away if the Tessian delegation attended the conference. In response, the Sami delegation officially announced that it would definitely attend if both the Daquan and Kephrian delegations stayed away.
If the statements given are all true and all the delegations adhered to their official announcements, it must also be true that the

• A. Daquan delegation attended the conference
• B. Daquan delegation did not attend the conference
• C. Sami government had no grievance against Tessia
• D. Tessian delegation did not attend the conference
• E. Tessian delegation made no official announcement regarding its attendance at the conference

Hint:

In formal logic problems, the contrapositive is a powerful tool. If you have a rule "If A then B" and you know that B is false, you can definitively conclude that A must also be false. This is often the key to solving complex chains of deductions.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a logical deduction problem based on a set of conditional statements ("if...then..."). We are given a final outcome and must work backward to determine what must have happened.

Step 2: Formalize the Statements
Let's use symbols for the delegations attending: S (Sami), K (Kephrian), D (Daquan), T (Tessian). \(\neg\) means "did not attend."

• Fact: \(\neg S\) and \(\neg K\). (Sami and Kephrian did not attend).
• Rule 1 (Daquan/Kephrian): If \(T\), then \(\neg D\) or \(\neg K\). (If Tessia attends, at least one of Daquan/Kephrian stays away).
• Rule 2 (Sami): If \(\neg D\) and \(\neg K\), then \(S\). (If both Daquan and Kephrian stay away, Sami attends).

Step 3: Deductions

1. Facts: Sami did not attend (\(\neg S\)). Kephrian did not attend (\(\neg K\)).
2. Sami Rule: \((\neg D \land \neg K) \rightarrow S\).
   Contrapositive: \(\neg S \rightarrow (D \lor K)\).
3. Since \(\neg S\) is true, we deduce \((D \lor K)\). But \(\neg K\) is also true.
   Therefore, \(D\) must be true. So, Daquan attended.
4. D\&K Rule: \(T \rightarrow (\neg D \lor \neg K)\).
   With \(D\) true and \(\neg K\) true, the conclusion \((\neg D \lor \neg K)\) is true.
   Hence the rule holds regardless of whether \(T\) is true or false.
   Therefore, Tessia’s attendance cannot be determined.

Checking the options:
 

• (A) Daquan attended: Must be true.
• (B) Daquan did not attend: False.
• (C) Tessia attended: Cannot be determined.
• (D) Tessia did not attend: Cannot be determined.

Final Answer:
\[ \boxed{\text{(A) Daquan delegation attended the conference. This follows directly from the rules, while Tessia’s status cannot be deduced.}} \]