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. (N ∪ R) ∩ M

Verified step by step guidance

1. First, identify the sets involved in the expression: N, R, and M. Recall their elements: N = {1, 3, 5, 7, 9, 11, 13}, R = {0, 1, 2, 3, 4}, and M = {0, 2, 4, 6, 8}.
2. Next, find the union of sets N and R, denoted as \(N \cup R\). The union includes all elements that are in N, or in R, or in both.
3. After finding \(N \cup R\), find the intersection of this union with set M, denoted as \((N \cup R) \cap M\). The intersection includes only the elements that are common to both \(N \cup R\) and M.
4. List the elements of \((N \cup R) \cap M\) explicitly by comparing the elements of \(N \cup R\) and M.
5. Finally, to identify any disjoint sets, check if the intersection of any two sets is empty. Two sets are disjoint if they have no elements in common.

Key Concepts

Set Union ( ∪ )

The union of two sets combines all unique elements from both sets. For example, A ∪ B includes every element that is in A, or in B, or in both. This operation helps to merge sets without duplication.

Set Intersection ( ∩ )

The intersection of two sets consists of elements common to both sets. For example, A ∩ B contains only those elements that appear in both A and B. This operation identifies shared elements between sets.

Disjoint Sets

Two sets are disjoint if they have no elements in common, meaning their intersection is the empty set. Identifying disjoint sets helps understand relationships and separations between groups of elements.