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. M ∩ R

Verified step by step guidance

1. Identify the sets M and R from the problem: M = {0, 2, 4, 6, 8} and R = {0, 1, 2, 3, 4}.
2. Recall that the intersection of two sets, denoted by \(M \cap R\), is the set of all elements that are common to both M and R.
3. Compare each element of set M with the elements of set R to find which elements appear in both sets.
4. List all elements that are found in both M and R to form the intersection set \(M \cap R\).
5. To identify if M and R are disjoint, check if their intersection \(M \cap R\) is the empty set \(\emptyset\). If it is empty, the sets are disjoint; otherwise, they are not.

Key Concepts

Set Intersection

The intersection of two sets includes all elements that are common to both sets. It is denoted by the symbol ∩. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}. Understanding intersection helps identify shared elements between sets.

Disjoint Sets

Disjoint sets are two or more 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 ∩ B = ∅, so A and B are disjoint. Recognizing disjoint sets is important for understanding relationships between sets.

Set Notation and Elements

Set notation uses curly braces {} to list elements, and elements are distinct objects within a set. Understanding how to read and interpret sets, such as U, M, N, Q, and R, is essential for performing operations like intersection and identifying relationships like disjointness.