What does A ∪ B represent in set notation?

What does A ∪ B represent in set notation?

• A. All the elements in both set A and set B
• B. All the elements in either set A or set B
• C. All elements not in set A
• D. The overlap of set A and set B

Answer: (B)

In set notation, A ∪ B represents the union of sets A and B. The union includes all the elements that are in either set A, set B, or in both sets. This means that if an element is found in at least one of the two sets, it will be included in the resulting set from the union. For example, if set A contains the elements {1, 2, 3} and set B contains the elements {3, 4, 5}, then A ∪ B will consist of {1, 2, 3, 4, 5}. This clearly demonstrates that the union combines all unique elements from both sets. This interpretation is vital in understanding set operations, and it articulates a fundamental concept in set theory that applies across various mathematical contexts.

In set notation, A ∪ B represents the union of sets A and B. The union includes all the elements that are in either set A, set B, or in both sets. This means that if an element is found in at least one of the two sets, it will be included in the resulting set from the union.

For example, if set A contains the elements {1, 2, 3} and set B contains the elements {3, 4, 5}, then A ∪ B will consist of {1, 2, 3, 4, 5}. This clearly demonstrates that the union combines all unique elements from both sets.

This interpretation is vital in understanding set operations, and it articulates a fundamental concept in set theory that applies across various mathematical contexts.