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 ∉ R}

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 $$R. $$This is the set difference $$U \setminus R. $$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 $$B. $$Symbolically, $$A \setminus B = \{ x \mid x \in A 	ext{ and } x 
otin B \}. $$Identify the elements of $$U$$ and $$R$$: $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$$ and $$R = \{0, 1, 2, 3, 4\}. $$Find the elements in $$U$$ that are not in $$R$$: Go through each element of $$U$$ and exclude those that appear in $$R. $$This will give the set $$\{ x \mid x \in U, x 
otin R \}. $$After finding the set difference, check if this resulting set is disjoint with any of the other given sets $$M$$, $$N$$, $$Q$$, or $$R. $$Two sets are disjoint if they have no elements in common.

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 ∉ R}

Verified video answer for a similar problem:

Key Concepts

Set Notation and Membership

Set Difference

Disjoint Sets