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

Verified step by step guidance

1. Identify the elements in set N: \{1, 3, 5, 7, 9, 11, 13\}.
2. Identify the elements in set R: \{0, 1, 2, 3, 4\}.
3. The union of two sets, N \cup R, includes all elements that are in either set N or set R or in both.
4. List all unique elements from both sets: \{0, 1, 2, 3, 4, 5, 7, 9, 11, 13\}.
5. Check if there are any common elements between N and R to determine if they are disjoint. Since they share elements, they are not disjoint.

Key Concepts

Set Theory

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. In this context, understanding how to manipulate sets—such as performing unions, intersections, and identifying disjoint sets—is crucial. A union combines all elements from the involved sets, while disjoint sets have no elements in common.

Union of Sets

The union of two or more sets is a new set that contains all the distinct elements from the original sets. For example, if we take sets N and R, their union, denoted as N ∪ R, will include every unique element from both sets. This concept is essential for solving the question as it requires combining the elements of the specified sets.

Disjoint Sets

Disjoint sets are sets that have no elements in common. Identifying disjoint sets is important in set theory as it helps in understanding the relationships between different sets. In the given question, recognizing which sets are disjoint can aid in analyzing their unions and intersections effectively.