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. M′ ∩ Q

Accepted Answer

Step 1: Understand the universal set and the given subsets. The universal set is $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\}$$, and the subsets are $$M = \{0, 2, 4, 6, 8\}$$ and $$Q = \{0, 2, 4, 6, 8, 10, 12\}. $$Step 2: Find the complement of set $$M$$, denoted $$M'. $$The complement $$M'$$ consists of all elements in $$U$$ that are not in $$M. So$$, $$M' = U \setminus M. $$Step 3: Write out the elements of $$M'$$ explicitly by removing all elements of $$M$$ from $$U. $$This means listing all elements of $$U$$ that are not in $$\{0, 2, 4, 6, 8\}. $$Step 4: Find the intersection of $$M'$$ and $$Q$$, denoted $$M' \cap Q. $$This means identifying all elements that are common to both $$M'$$ and $$Q. $$Step 5: List the elements that appear in both $$M'$$ and $$Q. $$These elements form the set $$M' \cap Q. $$After this, check if $$M'$$ and $$Q$$ have any elements in common; if none, they are disjoint sets.

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. M′ ∩ Q

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Key Concepts

Universal Set and Complement

Set Intersection

Disjoint Sets