What does it mean if we say that x is an element of A ∪ B?
Understand the Problem
The question is asking about the meaning of an element belonging to the union of two sets A and B, specifically what it implies about the element x's membership in either or both of the sets.
Answer
x is in set A, set B, or both.
The statement x ∈ A ∪ B means that x is an element of set A, or an element of set B, or an element of both sets A and B.
Answer for screen readers
The statement x ∈ A ∪ B means that x is an element of set A, or an element of set B, or an element of both sets A and B.
More Information
The union of two sets, denoted by A ∪ B, contains all elements that are in either one of the sets or in both. It is one of the fundamental concepts in set theory, helping to understand how different sets relate to each other.
Tips
A common mistake is to think that x must be in both sets A and B to be in the union, which is incorrect.
Sources
- Union, Intersection, and Complement | Mathematics for the Liberal Arts - courses.lumenlearning.com
- 1.1 Set theory | MATH0007: Algebra for Joint Honours Students - ucl.ac.uk
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