• If an element belongs to a set we write ∈, and if it does not belong we write ∉.
• For example, if A = {1, 2, 3}, then 2 ∈ A and 5 ∉ A.
• A set B is a subset of A if every element of B is also an element of A. We write B ⊆ A. For example, {1, 2} ⊆ {1, 2, 3}.
• The empty set is the set with no elements.
• It is written ∅ or { }.
• It has 0 elements, and it is a subset of every set, so ∅ ⊆ A always.

The universal set

• The universal set U contains all the elements under study.
• It is usually drawn as a large rectangle, and the other sets are drawn as circles inside it.