Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. ∅ ∩ Q

Key Concepts

Sets and Set Notation

A set is a collection of distinct objects, considered as an object in its own right. Set notation is used to define and describe these collections, using curly braces to list elements. For example, the set M = {0, 2, 4, 6, 8} contains even numbers from 0 to 8. Understanding how to read and interpret set notation is crucial for solving problems involving sets.

Intersection of Sets

The intersection of two sets, denoted as A ∩ B, is the set of elements that are common to both A and B. For instance, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}. This concept is essential for determining shared elements between sets, which is a key part of the question.

Disjoint Sets

Disjoint sets are sets that have no elements in common, meaning their intersection is the empty set (∅). For example, if A = {1, 2} and B = {3, 4}, then A and B are disjoint because A ∩ B = ∅. Identifying disjoint sets is important for understanding relationships between different sets in the context of the problem.