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

Accepted Answer

Understand the problem: You are given several sets and asked to find the intersection of the empty set ∅ and the set Q, and to identify any disjoint sets. The empty set ∅ contains no elements. Recall the definition of intersection: The intersection of two sets A and B, denoted by $$A \cap B$$, is the set of all elements that are common to both A and B. Apply the intersection operation to the empty set and Q: Since the empty set has no elements, there are no elements that can be common with any other set. Therefore, $$\emptyset \cap Q = \emptyset. $$Interpret the result: The intersection of the empty set with any set is always the empty set, which means they have no elements in common. Identify disjoint sets: Two sets are disjoint if their intersection is the empty set. Since $$\emptyset$$ has no elements, it is disjoint with every set, including Q.

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

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Key Concepts

Set Intersection

Empty Set (∅)

Disjoint Sets