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.