Understanding the Union of Sets in Mathematics: Definition, Examples, and Properties

(U)nion

In mathematics, the term “union” refers to the combination or merging of two or more sets to form a new set

In mathematics, the term “union” refers to the combination or merging of two or more sets to form a new set. It is denoted by the symbol “∪”.

If we have two sets A and B, the union of A and B, denoted as A ∪ B, is the set that contains all the elements that are in A, in B, or in both. In other words, it includes all the unique elements from both sets, without duplication.

For example, let’s say we have two sets:
A = {1, 2, 3}
B = {2, 3, 4}

To find the union of A and B (A ∪ B), we simply combine all the elements from both sets, without repeating any repeated elements:
A ∪ B = {1, 2, 3, 4}

Notice that the elements 2 and 3 are included only once, even though they were present in both sets. The union represents the entirety of the elements from both sets without repetition.

It is important to note that the union of two sets also includes all the elements from each set individually. So if a set has some elements that are not present in the other set, those elements will also be included in the union.

For example, let’s consider two more sets:
C = {1, 2, 3, 4}
D = {5, 6, 7}

The union of C and D (C ∪ D) will include all the elements from both sets:
C ∪ D = {1, 2, 3, 4, 5, 6, 7}

In this case, since C has elements that are not present in D (1, 2, 3, 4), those elements are also included in the union.

To summarize, the union of two sets combines all the unique elements from both sets into a new set without repetition, including any unique elements that are present in each set individually.

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