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