diff --git a/python/semantic_kernel/contents/utils/hashing.py b/python/semantic_kernel/contents/utils/hashing.py
index 02b341427027..738fe06a5a08 100644
--- a/python/semantic_kernel/contents/utils/hashing.py
+++ b/python/semantic_kernel/contents/utils/hashing.py
@@ -41,8 +41,15 @@ def make_hashable(input: Any, visited=None) -> Any:
         visited[unique_obj_id] = items
         return items
 
-    # Convert lists, sets, and tuples to tuples
-    if isinstance(input, (list, set, tuple)):
+    # Preserve unordered equality for sets, including equality with frozensets.
+    if isinstance(input, (set, frozenset)):
+        visited[unique_obj_id] = None
+        set_items = frozenset(make_hashable(item, visited) for item in input)
+        visited[unique_obj_id] = set_items
+        return set_items
+
+    # Convert ordered sequences to tuples.
+    if isinstance(input, (list, tuple)):
         visited[unique_obj_id] = None
         items = tuple(make_hashable(item, visited) for item in input)
         visited[unique_obj_id] = items
diff --git a/python/tests/unit/agents/chat_completion/test_chat_history_channel.py b/python/tests/unit/agents/chat_completion/test_chat_history_channel.py
index 7287456db127..02b3eac948da 100644
--- a/python/tests/unit/agents/chat_completion/test_chat_history_channel.py
+++ b/python/tests/unit/agents/chat_completion/test_chat_history_channel.py
@@ -250,3 +250,27 @@ async def test_receive_skips_file_references(chat_history_channel):
     assert len(channel.messages[2].items) == 2
     assert channel.messages[2].items[0].result == "normal content 2"
     assert channel.messages[2].items[1].text == "Normal message"
+
+
+async def test_invoke_deduplicates_equal_set_results(chat_history_channel):
+    """Equivalent set results must not be appended twice by the channel."""
+    channel = chat_history_channel
+    channel.add_user_message("Look up the values")
+    stored = ChatMessageContent(
+        role=AuthorRole.TOOL,
+        items=[FunctionResultContent(id="call", name="lookup", result=set([0, 8]))],
+    )
+    returned = ChatMessageContent(
+        role=AuthorRole.TOOL,
+        items=[FunctionResultContent(id="call", name="lookup", result=set([8, 0]))],
+    )
+    assert stored == returned
+
+    class AgentWithHistoryMutation:
+        async def invoke(self, **kwargs):
+            channel.messages.append(stored)
+            yield AgentResponseItem(message=returned, thread=channel.thread)
+
+    received = [message async for _, message in channel.invoke(AgentWithHistoryMutation())]
+    assert received == [stored]
+    assert channel.messages == [channel.messages[0], stored]
diff --git a/python/tests/unit/contents/test_hashing_utils.py b/python/tests/unit/contents/test_hashing_utils.py
index 66bcf52c13d9..02a45ff3088e 100644
--- a/python/tests/unit/contents/test_hashing_utils.py
+++ b/python/tests/unit/contents/test_hashing_utils.py
@@ -194,3 +194,36 @@ def test_hash_function_call_content():
     )
 
     _ = hash(content)
+
+
+def test_equal_sets_have_equal_hashes():
+    """Set iteration order must not affect function-result hashes."""
+    first = FunctionResultContent(id="call", name="lookup", result=set([0, 8]))
+    second = FunctionResultContent(id="call", name="lookup", result=set([8, 0]))
+    assert first == second
+    assert hash(first) == hash(second)
+    assert second in {first}
+
+
+def test_set_and_frozenset_have_equal_hashes():
+    """Python treats a set and a frozenset with equal elements as equal."""
+    first = FunctionResultContent(id="call", name="lookup", result={0, 8})
+    second = FunctionResultContent(id="call", name="lookup", result=frozenset({0, 8}))
+    assert first == second
+    assert hash(first) == hash(second)
+
+
+def test_nested_equal_sets_have_equal_hashes():
+    """Sets nested in function results retain unordered equality."""
+    first = FunctionResultContent(id="call", name="lookup", result={"values": [set([0, 8])]})
+    second = FunctionResultContent(id="call", name="lookup", result={"values": [set([8, 0])]})
+    assert first == second
+    assert hash(first) == hash(second)
+
+
+def test_mixed_set_elements_can_be_hashed():
+    """Unordered hashing must not require ordering unlike element types."""
+    first = FunctionResultContent(id="call", name="lookup", result={1, "one", (2, 3)})
+    second = FunctionResultContent(id="call", name="lookup", result=frozenset({1, "one", (2, 3)}))
+    assert first == second
+    assert hash(first) == hash(second)