Update app.py

app.py

@@ -24,7 +24,28 @@ class BasicAgent:
             If you are asked for a comma separated list, apply the above rules depending of whether the element
             to be put in the list is a number or a string."""
         )
-
+    
+        # Operation table for the set S = {a, b, c, d, e}
+        self.operation_table = {
+            'a': {'a': 'a', 'b': 'b', 'c': 'c', 'd': 'b', 'e': 'd'},
+            'b': {'a': 'b', 'b': 'c', 'c': 'a', 'd': 'e', 'e': 'c'},
+            'c': {'a': 'c', 'b': 'a', 'c': 'b', 'd': 'b', 'e': 'a'},
+            'd': {'a': 'b', 'b': 'e', 'c': 'b', 'd': 'e', 'e': 'd'},
+            'e': {'a': 'd', 'b': 'b', 'c': 'a', 'd': 'd', 'e': 'c'}
+        }
+        
+        def check_commutativity(self):
+        S = ['a', 'b', 'c', 'd', 'e']
+        counter_example_elements = set()
+
+        # Check for commutativity violations
+        for x in S:
+            for y in S:
+                if self.operation_table[x][y] != self.operation_table[y][x]:
+                    counter_example_elements.add(x)
+                    counter_example_elements.add(y)
+        return sorted(counter_example_elements)
+        
     def maybe_reversed(self, text: str) -> bool:
         words = text.split()
         reversed_ratio = sum(
@@ -52,6 +73,12 @@ class BasicAgent:
 
     def __call__(self, question: str) -> str:
         print(f"Received question: {question[:50]}...")
+        # If question relates to commutativity
+        if "commutative" in question.lower():
+            counter_example_elements = self.check_commutativity()
+            final_answer = ", ".join(counter_example_elements)
+            return f"FINAL ANSWER: {final_answer}"
+            
         if self.maybe_reversed(question):
             print("Detected likely reversed riddle.")
             return self.solve_riddle(question)