DOC: Fix doc for first_valid_index (pandas-dev#55236)

* Fix doc for first_valid_index

* Replace notes with examples

* Add explicit prints

pandas/core/generic.py

@@ -12466,11 +12466,6 @@ def first_valid_index(self) -> Hashable | None:
         -------
         type of index
 
-        Notes
-        -----
-        If all elements are non-NA/null, returns None.
-        Also returns None for empty {klass}.
-
         Examples
         --------
         For Series:
@@ -12481,6 +12476,22 @@ def first_valid_index(self) -> Hashable | None:
         >>> s.last_valid_index()
         2
 
+        >>> s = pd.Series([None, None])
+        >>> print(s.first_valid_index())
+        None
+        >>> print(s.last_valid_index())
+        None
+
+        If all elements in Series are NA/null, returns None.
+
+        >>> s = pd.Series()
+        >>> print(s.first_valid_index())
+        None
+        >>> print(s.last_valid_index())
+        None
+
+        If Series is empty, returns None.
+
         For DataFrame:
 
         >>> df = pd.DataFrame({{'A': [None, None, 2], 'B': [None, 3, 4]}})
@@ -12493,6 +12504,31 @@ def first_valid_index(self) -> Hashable | None:
         1
         >>> df.last_valid_index()
         2
+
+        >>> df = pd.DataFrame({{'A': [None, None, None], 'B': [None, None, None]}})
+        >>> df
+             A      B
+        0  None   None
+        1  None   None
+        2  None   None
+        >>> print(df.first_valid_index())
+        None
+        >>> print(df.last_valid_index())
+        None
+
+        If all elements in DataFrame are NA/null, returns None.
+
+        >>> df = pd.DataFrame()
+        >>> df
+        Empty DataFrame
+        Columns: []
+        Index: []
+        >>> print(df.first_valid_index())
+        None
+        >>> print(df.last_valid_index())
+        None
+
+        If DataFrame is empty, returns None.
         """
         return self._find_valid_index(how="first")