Inclusion Relation
Order relation between two sets A and B in which we say that set A is included in set B if and only if all of the elements of A are also elements of B.
Symbols
The symbol "⊆" is read as: "…is included in…" or "...is a subset of…". If we have A ⊆ B, this means that all of the elements of A are in B or that A is equal to B. The symbol "⊂" is read as: "...is strictly included in…" or "...is a strict subset of…". If we have A ⊂ B, this means that all of the elements of A are in B but that at least one element of B is not in A.Properties
- Every set is included in itself.
- The empty set is included in every set.
Examples
- If A = {2, 3, 4} and B = {3, 4, 5, 6}, then: A ∩ B = {3, 4} and A ∪ B = {2, 3, 4, 5, 6}. We can say that (A ∩ B) ⊂ (A ∪ B).
- If A = {4, 5, 6, 7} and B = {3, 4, 5, 6, 7, 8}, then A ⊂ B.
- If A = {4, 5, 6, 7} and B = {4, 5, 6, 7}, then A ⊆ B.