Inclusion Relation

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 A is not in B.

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.

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