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 ∩ R′

Verified step by step guidance

1. Identify the universal set $U=\{0,1,2,3,4,5,6,7,8,9,10,11,12,13\}$.
2. Determine the complement of set $R$, denoted as $R^{\prime }$, which includes all elements in $U$ that are not in $R$.
3. Calculate $R^{\prime }=U-R=\{5,6,7,8,9,10,11,12,13\}$.
4. Find the intersection of sets $Q$ and $R^{\prime }$, denoted as $Q\cap R^{\prime }$.
5. List the common elements between $Q=\{0,2,4,6,8,10,12\}$ and $R^{\prime }=\{5,6,7,8,9,10,11,12,13\}$.

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 denote the elements. Understanding how to read and write sets is crucial for performing operations such as unions, intersections, and complements.

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 a key operation in set theory. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.

Complement of a Set

The complement of a set A, denoted as A′, consists of all elements in the universal set U that are not in A. This concept helps in understanding the relationship between a set and the universal set, allowing for operations that involve elements outside of a given set. For instance, if U = {0, 1, 2, 3, 4} and A = {1, 2}, then A′ = {0, 3, 4}.