How many subsets are there in 12 elements?

Answer 1

A set with 12 elements has 212 = 4096 subsets, including the null set (no elements) and the original full set, which is not a proper subset of itself.

Here's the logic behind it:

• In making up a subset, you have a two-way choice for each element: to include it or to exclude it.
• These choices are independent: whether or not you include, say, element #4 doesn't depend in any way on your choices for the other 11.
• So you have
• 1. two choices for element #1 (in or out)
  2. Then you have two choices for element #2. Combined with the two for #1, that makes four: in-in {1,2}, in-out {1}, out-in {2}, out-out {} (the null set, Ø).
  3. And you have two choices for #3... which makes 8 possibilities...
  4. and so on...
• ... till you have 2x2x2x2x2x2x2x2x2x2x2x2 = 212 = 4096 possible subsets.