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Subset Calculator

Check subset and proper subset relationships between sets

📐Subset Definitions

Subset (A ⊆ B)
Every element of A is in B
A can equal B
Proper Subset (A ⊂ B)
A ⊆ B and A ≠ B
At least one element in B not in A
Empty Set
∅ is a subset of every set
Including itself
Equal Sets
A = B if A ⊆ B and B ⊆ A
Same elements in both

💡Subset Examples

{1, 2} ⊆ {1, 2, 3}
True - proper subset
All elements of first are in second
{1, 2} ⊆ {1, 2}
True - but not proper
Sets are equal
{1, 4} ⊆ {1, 2, 3}
False
4 is not in second set
∅ ⊆ {1, 2}
True - always
Empty set is subset of all sets

💼Applications

Mathematics
• Set theory
• Proof techniques
• Relations
Computer Science
• Database queries
• Set operations
• Data structures
Logic
• Boolean algebra
• Venn diagrams
• Set membership

🔢Subset Properties

• Reflexive: A ⊆ A for any set A
• Transitive: If A ⊆ B and B ⊆ C, then A ⊆ C
• Anti-symmetric: If A ⊆ B and B ⊆ A, then A = B
• Empty set: ∅ ⊆ A for any set A
• Every set is a subset of itself

Subset Calculator