What it does
A subset of a set A is any collection of A’s elements, including none of them (the empty set ∅) and all of them (A itself). The set of all subsets of A is its power set, P(A). This page lists P(A) for any set you type, up to 6 elements, and shows where the famous count comes from: a set with n elements has 2ⁿ subsets.
The reason is a string of yes/no choices. To make a subset, go through the elements one at a time and decide: in or out? Two choices for the first element, two for the second, and so on, so 2 × 2 × … × 2 = 2ⁿ subsets in all. The page draws this as a tree (for up to 4 elements) and lets you make the choices yourself with switches.
It fits the Class 11 maths chapter on sets (subsets and power sets), and the counts by size, C(n, k), lead into permutations and combinations and the binomial theorem later in Class 11.
The venn diagram calculator tool shows unions and intersections of the subsets you find here; the counts 1, 4, 6, 4, 1 come back as coefficients in the binomial expansion.
How to use it
- Type the elements, separated by commas (or spaces). Braces are fine: {1, 2, 3}. Repeats are left out, and the page tells you so, because a set lists each element once. Or tap one of the example sets.
- Under Build one subset, tap each element to switch it in or out. Your subset appears with its switch code (1 = in, 0 = out), its path is drawn thick in the tree, and it is highlighted in the full list.
- All the subsets, by size puts the subsets in columns: none, one, two … elements. Each column’s heading gives its count C(n, k), the number of ways to choose k of the n elements.
- The box at the bottom adds it up: 2ⁿ subsets, 2ⁿ − 1 proper subsets, the counts by size, and the fact that exactly half of the subsets contain any given element.
Worked example
The page opens on {a, b, c}. The title says it has 3 elements, so 2³ = 8 subsets. The columns read:
- 0 elements, C(3, 0) = 1: ∅
- 1 element, C(3, 1) = 3: {a}, {b}, {c}
- 2 elements, C(3, 2) = 3: {a, b}, {a, c}, {b, c}
- 3 elements, C(3, 3) = 1: {a, b, c}
The bottom box gives 1 + 3 + 3 + 1 = 8, 7 proper subsets, and 4 subsets that contain a. Tap a and c to switch them in: your subset is {a, c}, switch code 101, and the thick path in the tree goes right, left, right.
Tips
- ∅ is a subset of every set, and every set is a subset of itself.
- The elements of P(A) are sets. So {1} ∈ P({1, 2}), but 1 is not an element of P({1, 2}).
- Adding one element doubles the number of subsets: each old subset appears again with the new element added.
FAQ
Why only up to 6 elements? Seven elements already give 128 subsets, which no longer fits on a phone screen in a useful way. The rule 2ⁿ works for any n.
What is a proper subset? A subset that is not the whole set. There are 2ⁿ − 1 of them. (Some books also leave out ∅; then it is 2ⁿ − 2.)
Is anything saved? No. Everything runs in your browser. fibub is not part of NCERT; the topics follow the syllabus, but the words, pictures and examples are our own.
Where the numbers come from
- Subsets, power sets, the 2ⁿ rule and binomial coefficients are standard set theory and counting. Wording, pictures and examples are fibub's own; no textbook text, figures or exercises are used.
- Checked against Python's itertools.combinations (every subset, in order of size) and math.comb (the counts for sets of 0 to 6 elements).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.