Collection categories:

Union: A set with elements belonging to A or B as its elements is called the union of A and B, denoted by A∪B (or B∪A), read as "A and B" (or "B and A"), that is, A∪B={x|x∈A, or x∈B}

For example, the universe U={1, 2, 3, 4, 5} A={1, 3, 5} B={1, 2, 5}.

The two sets contain the five elements 1, 2, 3, 4, and 5. No matter how many times an element appears, as long as it appears in both sets, then A∪B={1, 2, 3, 5}. The shaded part in the figure is A∩B.

Intersection: The set whose elements belong to both A and B is called the intersection of A and B, denoted by A∩B (or B∩A), read as "A intersects B" (or "B intersects A"), that is, A∩B={x|x∈A, and x∈B}

For example, the set U={1, 2, 3, 4, 5} A={1, 3, 5} B={1, 2, 5}. Then, since both A and B contain 1 and 5, A∩B={1, 5}.

Difference: The set whose elements belong to A but not to B is called the difference between A and B.