U

The union of sets A and B, written A ∪ B, is the set of everything that is in A, or in B, or in both.

Precisely: A ∪ B = {x : x ∈ A or x ∈ B}; each element is listed once, even if it is in both sets.

How it works

Put the two sets together into one and cross out any repeats. In a Venn diagram, the union is everything inside either circle.

Examples

• The union of {1, 2, 3} and {3, 4} is {1, 2, 3, 4}.
• The union of the even numbers and the odd numbers is all the whole numbers.
• In a Venn diagram the union is the whole shaded area of both circles.
• n(A ∪ B) = n(A) + n(B) − n(A ∩ B) counts the union without double counting.

Do not confuse: The union takes everything in either set; the intersection takes only what is in both.

Used in

counting problems, probability of "A or B", Venn diagrams

Symbols

∪

Related

intersection (of sets), set, Venn diagram

From

Class 11 Mathematics, Chapter 1: Sets