Subsets
A subset is defined as a set that is wholly contained within another set. For example, if A = {1, 2, 3, 4} and B = {2, 3} then B is a subset of A. The symbol ⊆ is used to mean subset, so B ⊆ A reads ‘B is a subset of A’. The line in this symbol is reminiscent of an equals sign because a subset can technically have exactly the same elements as the superset. That is, if D = {1, 2, 3, 4} and E = {1, 2, 3, 4}, D = E and D ⊆ E are both true. A proper subset uses the symbol ⊂ and is defined as a subset where at least one element is in the superset that is not in the subset. For example, {1, 2, 3} is a proper subset of ℕ because there is at least one element in ℕ that is not in {1, 2, 3}.
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