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. Q ∩ (M ∪ N)

Accepted Answer

First, understand the problem: You are asked to find the intersection of set Q with the union of sets M and N, which is written as $$Q \cap (M \cup N). $$Step 1: Find the union of sets M and N. The union $$M \cup N$$ includes all elements that are in M, or in N, or in both. Write down all unique elements from M and N combined. Step 2: Once you have $$M \cup N$$, find the intersection with Q. The intersection $$Q \cap (M \cup N)$$ includes only those elements that are in both Q and $$M \cup N. $$Step 3: List the elements of Q and compare them with the elements of $$M \cup N to $$identify the common elements. Step 4: After finding the intersection, check if any of the sets involved are disjoint. Two sets are disjoint if their intersection is the empty set (no common elements).

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. Q ∩ (M ∪ N)

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Key Concepts

Set Union ( ∪ )

Set Intersection ( ∩ )

Disjoint Sets