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. {x | x ∈ M or x ∈ Q}

Verified step by step guidance

1. Understand the problem: We are given several sets and asked to find the set defined by {x | x \in M or x \in Q}, which means the union of sets M and Q.
2. Recall the definition of union of two sets: The union of sets M and Q, denoted by M \cup Q, is the set of all elements that are in M, or in Q, or in both.
3. List the elements of sets M and Q: M = {0, 2, 4, 6, 8} and Q = {0, 2, 4, 6, 8, 10, 12}.
4. Combine the elements of M and Q without repeating any element to form the union M \cup Q.
5. After forming the union, check if M and Q are disjoint by seeing if they have any common elements. If they share no elements, they are disjoint; otherwise, they are not.

Key Concepts

Set Union

The union of two sets combines all elements that belong to either set without duplication. For sets M and Q, the union M ∪ Q includes every element found in M, in Q, or in both. This operation helps in finding all unique elements from both sets.

Disjoint Sets

Disjoint sets are sets that have no elements in common. Identifying disjoint sets involves checking if their intersection is empty. This concept is important to determine whether two sets share any elements or are completely separate.

Set Notation and Membership

Set notation uses symbols like ∈ to indicate membership, meaning an element belongs to a set. Understanding this notation is essential to interpret expressions like {x | x ∈ M or x ∈ Q}, which describes all elements x that are in M or Q.