What does X ∩ Y represent in set theory?

In set theory, the notation X ∩ Y represents the intersection of two sets X and Y. The intersection refers to the set of elements that are common to both sets. For instance, if set X contains the elements {1, 2, 3} and set Y contains the elements {2, 3, 4}, then the intersection X ∩ Y would be the set {2, 3}, as those are the elements found in both sets.

Understanding intersections is fundamental in various applications of mathematics and logical reasoning, as it helps identify shared attributes among groups. By focusing on what is common, rather than what is distinct or combined, intersections are crucial for analyzing relationships between different sets.