Universal set

           We always consider all sets for the problem under consideration to be a subset of a (large) set called the universal set. For the binary digital communication problem, the set may be considered as the universal set. We shall denote the universal set by the symbol S.

Example 3

           In discussion involving English letters, the alphabet of the English language may be considered as the universal set.

Equality of two sets

          Two sets A and B are equal   if and only if  they have the same elements. Thus,

• A = B   if and only if     and   .   In other words,

We take above definition of the equality of two sets to establish identities involving set theoretic operation.