SET OPERATIONS

1. Union

The union of sets A and B is the set of all elements which belong to A or to B or to both. We denote the union of A and B by;

A∪B

Which is usually read “A union B”

Example 1.1: In the Venn diagram in fig 2-1, we have shaded A∪B,

i.e. the area of A and the area of B.

Example 1.2: Let S = {a, b. c. d} and T = {f, b, d, g}. 

Then S.         T = {a, b, c, d, f, g}.

Example 1.3: Let P be the set of positive real numbers and let Q be the set of negative real numbers. The P∪Q, the union of P and Q, consist of all the real numbers except zero. The union of A and B may also be defined concisely by:

A∪B = {xx∈A or x∈B}

Remark 2.1: It follows directly from the definition of the union of two sets that A∪B and B∪A are the same set, i.e.,

A∪B = B∪A

Remark 2.2: Both A and B are always subsets of A and B that is, 

A⊂ (A∪B) and B⊂ (A∪B)

In some books, the union of A and B is denoted by A + B and is called the settheoretic sum of A and B or, simply, A plus B