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′ ∩ Q

Key Concepts

Set Complement

The complement of a set, denoted as M′, consists of all elements in the universal set U that are not in set M. For example, if M = {0, 2, 4, 6, 8}, then M′ includes all elements from U that are not in M, which would be {1, 3, 5, 7, 9, 10, 11, 12, 13}. Understanding set complements is crucial for solving problems involving set operations.

Set Intersection

The intersection of two sets, denoted as A ∩ B, includes all elements that are common to both sets A and B. In this case, to find M′ ∩ Q, we need to identify the elements that are present in both the complement of M and set Q. This concept is fundamental in set theory as it helps in determining shared elements between different sets.

Disjoint Sets

Disjoint sets are sets that have no elements in common, meaning their intersection is the empty set. For example, if two sets A and B are disjoint, then A ∩ B = ∅. Identifying disjoint sets is important in set theory as it helps in understanding relationships between different groups of elements and can simplify various operations involving those sets.