Question

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 and x ∈ Q}

Accepted Answer

Understand the problem: We are given several sets and asked to find the set of elements $$ x $$ such that $$ x \in M $$ and $$ x \in Q . $$This means we need to find the intersection of sets $$ M $$ and $$ Q . $$Recall the definition of intersection: The intersection of two sets $$ A $$ and $$ B $$, denoted $$ A \cap B $$, is the set of all elements that are in both $$ A $$ and $$ B . So$$, $$ M \cap Q = \{ x \mid x \in M 	ext{ and } x \in Q \} . $$List the elements of each set explicitly: $$ M = \{0, 2, 4, 6, 8\} $$ and $$ Q = \{0, 2, 4, 6, 8, 10, 12\} . $$Compare the elements of $$ M $$ and $$ Q  to $$find common elements. Identify which elements appear in both sets. Write the intersection set $$ M \cap Q  as $$the set of all common elements found in the previous step. Then, check if $$ M $$ and $$ Q $$ are disjoint by verifying if their intersection is empty or not.

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 and x ∈ Q}

Verified video answer for a similar problem:

Key Concepts

Set Intersection

Disjoint Sets

Set Notation and Membership