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Intermediate ⛓ Discrete Math & Number Theory Topic 18 of 103

Subsets and Power Sets

A set with n elements has 2ⁿ subsets.

Key idea

A set with n elements has 2ⁿ subsets.

In depth

A ⊆ B means every element of A is in B. The power set P(A) is the set of all subsets of A; if |A| = n then |P(A)| = 2ⁿ, since each element is either in or out. The empty set is a subset of every set.

Worked example

P({a, b}) = {∅, {a}, {b}, {a, b}}, which has 4 elements.

Formula

|P(A)| = 2ⁿ

Real-world uses

Common mistake

Forgetting the empty set and the set itself.

How to learn this

  1. Read the key idea and say it in your own words.
  2. Work through the worked example, then try a similar problem.
  3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

What is Subsets and Power Sets?

A set with n elements has 2ⁿ subsets. It is a topic at the intermediate level in Discrete Math & Number Theory.

What is the formula for Subsets and Power Sets?

The key formula is |P(A)| = 2ⁿ.

Where is Subsets and Power Sets used in real life?

Real-world examples: Listing all possible combinations of toppings or features in a product configurator.

What should I learn before Subsets and Power Sets?

Make sure you are comfortable with Sets and Elements, the previous topic in Discrete Math & Number Theory.

What is a common mistake with Subsets and Power Sets?

Forgetting the empty set and the set itself.

How can I practise Subsets and Power Sets?

Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.

What comes after Subsets and Power Sets?

Move on to Set Operations next.

Related intermediate topics in Discrete Math & Number Theory