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 ∈ U, x ∉ M}

Accepted Answer

Understand the problem: We are given a universal set $$U$$ and several subsets $$M$$, $$N$$, $$Q$$, and $$R. $$The task is to find the set of all elements $$x$$ such that $$x is in$$ $$U$$ but not in $$M. $$This is the set difference $$U \setminus M. $$Recall the definition of set difference: For two sets $$A$$ and $$B$$, the difference $$A \setminus B is $$the set of all elements that are in $$A$$ but not in $$B. So $$here, $$U \setminus M = \{ x \mid x \in U 	ext{ and } x 
otin M \}. $$List the elements of $$U$$ and $$M$$ explicitly: $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$$ and $$M = \{0, 2, 4, 6, 8\}. $$Remove all elements of $$M$$ from $$U$$: Go through each element of $$U$$ and exclude those that appear in $$M. $$The remaining elements form the set $$U \setminus M. $$After finding $$U \setminus M$$, analyze the sets to identify any disjoint sets. Two sets are disjoint if they have no elements in common. Compare $$U \setminus M$$ with the other given sets $$N$$, $$Q$$, and $$R to $$check for disjointness.

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 ∈ U, x ∉ M}

Verified video answer for a similar problem:

Key Concepts

Set Notation and Set Builder Notation

Set Operations: Complement and Difference

Disjoint Sets