1.3.7.1 Union of Sets

The union of two sets is a set that contains all the distinct elements that are in either of the sets or in both. Mathematically, the union of sets  and  is denoted as   . A key aspect of the union is its inclusiveness. It doesn't matter if an element is in one set, the other, or both; if it's in either set, it's in the union. Another important aspect is that each element in the union is unique. Even if an element appears in both sets, in the union, it will only be counted once.

In set builder form, union of sets  and  is represented as:

This can be interpreted as “The union of sets  and , denoted by   , consists of all elements  such that  is an element of set , or  is an element of set ”. For instance, if  = {1, 2} and  = {2, 3}, then:

Example 1.18. Consider a university where the Science Department and the Environmental Studies Department each offer a range of courses. To understand the full spectrum of courses available across these two departments, we can use the concept of the union of sets.

Sets Definition:

• Set A: Courses offered in the Science Department = {Biology, Chemistry, Physics, Mathematics}
• Set B: Courses offered in the Environmental Studies Department = {Ecology, Environmental Science, Biology, Geology}