Subset take-away is a two player game played with a finite set of numbers. Players alternately choose nonempty subsets of with the conditions that a player may not choose the whole set or any set containing a set that was named earlier. The first player who is unable to move loses the game.

Verify that when has four elements, the second player still has a winning stragey still. Convince the reader (me) that the second player can win regardless of what the first player does. Feel free to argue in words and/or use Python in your arguement. If you choose to let the computer argue for you, the itertools library has a constructor cominations(iterable, r) which returns length subsequences of elements from the input iterable. Also, you can check if an element is in a Python set logically with x in Set. I'll demo a few ideas below, but you'll notice a formatting is a bit strange, because Python doesn't like sets within sets.