SET OPERATIONS

2. Intersection

The Intersection of sets A and B is the set of elements which are common to A and B, that is, those elements which belong to A and which belong to B. We denote the intersection of A and B by:

A∩B

Which is read “A intersection B”.

Example 2.1: In the Venn diagram in fig 2.2, we have shaded A∩B, the area that is common to both A and B

Example 2.2: Let S = {a, b, c, d} and T = {f, b, d, g}. Then S∩T = {b, d}

Example 2.3: Let V = 2, 3, 6, ......} i.e. the multiples of 2; and

Let W = {3, 6, 9,....} i.e. the multiples of 3. Then

                             V∩W = {6, 12, 18......}

The intersection of A and B may also be defined concisely by

                              A∩B = {x∈A, x∈B}

Here, the comma has the same meaning as “and”.

Remark 2.3: It follows directly from the definition of the intersection of two

sets that;

                           A∩B =B∩A

Remark 2.4:

Each of the sets A and B contains A∩B as a subset, i.e.,

               (A∩B)⊂A and (A∩B) ⊂B

Remark 2.5: If sets A and B have no elements in common, i.e. if A and B are disjoint, then the intersection of A and B is the null set, i.e. A∩B =∅

In some books, especially on probability, the intersection of A and B is denoted by AB and is called the set-theoretic product of A and B or, simply, A times B.