How many subsets does a set with elements have? For each element, you have 2 choices: include it or exclude it. By the product rule, the total is .
For , the 8 subsets are: . This includes the empty set and the full set.
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
The power of 2
How many subsets does a set with elements have? For each element, you have 2 choices: include it or exclude it. By the product rule, the total is .
For , the 8 subsets are: . This includes the empty set and the full set.