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Operations on Sets

You are already familiar with arithmetic operations, addition, subtraction and multiplication.

In this section, we shall learn the operations of union, intersection and difference of sets.

There are three basic set operations: intersection, union, and complementation.

The intersection of two sets is the set containing the elements common to both the sets and is denoted by the symbol .
The union of two sets is the set containing all elements belonging to either one of the sets or to both, denoted by the symbol .
Thus, if C = {1, 2, 3, 4} and D = {3, 4, 5}, then C ∩ D = {3, 4} and C  D = {1, 2, 3, 4, 5}. These two operations obey both the associative law and the commutative law, and also they obey the distributive law.

If the universal set U = {1, 2, 3, 4, 5} and A = {1, 2, 3}, then the complement of A (written A') is the set of all elements in the universal set that are not in A, or A' = {4, 5}.

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