Math Problem Statement

Solution

To solve the given problem, we need to find the union of sets MM and NN, and then complement this union with respect to the universal set UU.

The universal set UU is {0,1,2,4,6,8}\{0, 1, 2, 4, 6, 8\}. Set MM is {0,4,6}\{0, 4, 6\}. Set NN is {0,1,6}\{0, 1, 6\}.

First, we find the union of MM and NN: MN={0,4,6}{0,1,6}M \cup N = \{0, 4, 6\} \cup \{0, 1, 6\} ={0,1,4,6}= \{0, 1, 4, 6\}

Next, we find the complement of MNM \cup N with respect to UU. The complement of a set AA with respect to the universal set UU consists of all elements in UU that are not in AA:

MN={0,1,4,6}M \cup N = \{0, 1, 4, 6\}

The elements in UU that are not in MNM \cup N are: U(MN)={0,1,2,4,6,8}{0,1,4,6}U - (M \cup N) = \{0, 1, 2, 4, 6, 8\} - \{0, 1, 4, 6\} ={2,8}= \{2, 8\}

Thus, the complement of MNM \cup N with respect to UU is {2,8}\{2, 8\}.

Since {2,8}\{2, 8\} is not listed among the options, let's carefully recheck the elements of the union MNM \cup N:

Correctly listing all elements of MNM \cup N: MN={0,1,4,6}M \cup N = \{0, 1, 4, 6\}

Correctly identifying the complement: U(MN)={2,8}U - (M \cup N) = \{2, 8\}

Reviewing the problem step by step, we conclude that {2,8}\{2, 8\} was the result, however, none of the given options directly match this.

Let's verify this once again against the possible correct set options provided:

Correct Answer should be reconsidered for potential matching:

Correct option in set: U(MN)U - (M \cup N): U{0,1,4,6}={2,8}U - \{0, 1, 4, 6\} = \{2, 8\}

For Union correctly in listed options, it: Clearly does align in original.

Ensuring careful checking for correction and re-examining if stated clear again,

Please ensure specific accurate interpretation of steps noted correctly, options should logically match accurately as:

Possible, typically options now fact-check and inquired ensuring noting steps clearly exact as given per image scenario.

Do you want more details or have any questions? Here are 5 questions you might want to ask next:

  1. How do you find the complement of a set?
  2. Can you explain the union and intersection of sets?
  3. How are set operations used in probability?
  4. What are the different types of sets in mathematics?
  5. How do you solve problems involving universal sets?

Tip: When dealing with set operations, always carefully list out each element to avoid missing or duplicating elements in the union, intersection, or complement.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Union of Sets
Complement of Sets

Formulas

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Theorems

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Suitable Grade Level

High School