Which of the following represents the union of sets A and B in a Venn Diagram?

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Study for the Western Governors University (WGU) MATH1709 C277 Finite Mathematics Exam. Explore with flashcards and multiple-choice questions. Build a strong foundation and ace your exam with confidence!

The union of sets A and B, represented as A ∪ B, includes all elements that are in either set A, set B, or in both sets. In the context of a Venn Diagram, this means that the area shaded would cover every element that is within either of the circles representing the sets A and B.

When visualizing the two sets, the union encompasses the entire area of both circles, effectively collecting all unique elements from both sets without duplication. This is a fundamental principle of set theory that describes how to combine different collections of items into a single collection that includes everything from both.

In contrast, the intersection of the sets (A ∩ B) would only account for the elements common to both sets, while the difference (A - B) removes the elements in set B from set A. The complement intersection (A' ∩ B') includes elements outside of A and B, which does not reflect the requirement to combine the two sets. Therefore, A ∪ B correctly captures the intended concept of union in a Venn Diagram.

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