What does A' denote in set theory?

In set theory, A' represents the complement of set A. The complement includes all elements that are not in set A but are part of the universal set that contains all possible elements relevant to the discussion.

To put it more simply, if you imagine a universal set U that includes all elements under consideration, the complement of A (A') consists of every element in U that is excluded from A. For example, if the universal set were the numbers 1 to 10, and set A included the numbers 2, 3, and 5, then A' would include the numbers 1, 4, 6, 7, 8, 9, and 10.

This concept is fundamental in set theory, as it allows for the examination of what is outside a given set, which can be useful in various mathematical applications, such as probability and logic. Understanding the complement helps to clarify relationships between different sets and their elements, making it critical to grasp the notation and its implications in mathematical problems involving sets.