Practice question · Put in order
Arrange these sets in order of increasing size.
- The power set of a set with 2 elements
- A set with 2 elements
- The power set of a set with 3 elements
- The power set of a set with 4 elements
Hints
- The power set of an n-element set has 2 to the power n members.
- That gives 2, 4, 8 and 16 respectively.
Show the answer
- A set with 2 elements
- The power set of a set with 2 elements
- The power set of a set with 3 elements
- The power set of a set with 4 elements
Why
Sizes 2, 4, 8, 16. Each power set is strictly larger than the set it came from, which is Cantor’s theorem in its finite and least surprising form.
Practise Relations, Functions and Power Sets
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