SET004 · Sets, relations & logic · Classes 9–11
Subset
A is a subset of B (A ⊆ B) when every element of A is also in B. In a Venn diagram, A sits inside B.
A ⊆ BSubset
📐 Formula
A ⊆ B ⇔ (x ∈ A ⇒ x ∈ B); a set with n elements has 2ⁿ subsets
✏️ Worked example
Multiples of 4 up to 24 are all multiples of 2, so A ⊆ B.
🌍 Where it is used
Categories: every square is a rectangle, so squares ⊆ rectangles.
❓ Quick check
How many subsets does {a, b, c} have?
🏋️ Practice
EasyIs {1, 2} ⊆ {1, 2, 3}?
Answer: Yes
MediumIs ∅ a subset of every set?
Answer: Yes
ChallengeList the subsets of {x, y}.
Answer: ∅, {x}, {y}, {x, y}