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 elements in set M: \( M = \{0, 2, 4, 6, 8\} \).
2. Identify the elements in set R: \( R = \{0, 1, 2, 3, 4\} \).
3. Find the intersection of sets M and R, denoted as \( M \cap R \).
4. The intersection \( M \cap R \) consists of elements that are common to both sets M and R.
5. List the common elements from both sets to determine \( M \cap R \).

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 symbols like braces {} to enclose elements. Understanding how to read and write sets is crucial for performing operations such as unions, intersections, and differences.

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. This concept is essential for determining shared elements between sets, which is particularly relevant in the given question where we need to find M ∩ R. Knowing how to compute intersections helps in analyzing relationships between different sets.

Disjoint Sets

Disjoint sets are sets that have no elements in common, meaning their intersection is the empty set (A ∩ B = ∅). Identifying disjoint sets is important in various applications, such as probability and statistics, as it helps in understanding the relationships and distinctions between different groups. In the context of the question, recognizing disjoint sets aids in analyzing the provided sets effectively.