Practice question · True or false
A set with 3 elements has 8 subsets because each element is independently either in or out.
Hints
- How many binary choices is that?
- .
Show the answer
True
Why
True. Each element contributes an independent in-or-out choice, giving subsets, 8 for three elements. The same counting argument shows why the power set is strictly larger than the set, which is the finite shadow of Cantor's theorem.
Practise Sets and Set-Builder Notation
The app has 4 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Sets and Set-Builder Notation
- For A = {1, 2}, both 1 ∈ A and {1} ∈ A are true.
- Is there a set of all sets? Russell asked instead about the set of all sets that do not contain themselves.…
- For any set A, both ∅ subseteq A and ∅ ∈ A hold.
- Sort each object by whether it belongs to the set S = { x : x is an integer and x squared < 10 }.
- {x : x ∈ ℝ, x² = -1} and {x : x ∈ ℤ, 0 < x < 1} are both empty. Why is there only ONE empty set rather than…
- For A = {1, 2}, the statement "{1} is a subset of A" is true while "{1} is an element of A" is false. Why…