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A = {1, 2, 5, 7, 9}, B = {1, 3, 4, 7, 8} C = {3,4,6,8} Verify by direct computation each equa a. AU (BUC) = (AUB) UC b. An (BNC) = (ANB) nC

A = {1, 2, 5, 7, 9}, B = {1, 3, 4, 7, 8} C = {3,4,6,8} Verify by direct computation each equa a. AU (BUC) = (AUB) UC b. An (BNC) = (ANB) nC

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The text comprises a mathematical exercise about set theory. Below is the transcription tailored for an educational website setting: --- **Exercise: Verification of Set Equations** Consider the following sets: - \( A = \{1, 2, 5, 7, 9\} \) - \( B = \{1, 3, 4, 7, 8\} \) - \( C = \{3, 4, 6, 8\} \) **Objective:** Verify each equation using direct computation. a. Verify the equation: \( A \cup (B \cup C) = (A \cup B) \cup C \) b. Verify the equation: \( A \cap (B \cap C) = (A \cap B) \cap C \) **Instructions:** 1. **Union (\( \cup \)) and Intersection (\( \cap \)) Operations:** - **Union (\( \cup \))**: The set containing all distinct elements present in any of the sets involved. - **Intersection (\( \cap \))**: The set containing all elements common to all sets involved. 2. **Verify Each Side of the Equations:** - Compute the left-hand side and right-hand side of each equation and check for equality. **Additional Notes:** - Detail each step carefully to ensure accuracy. - Use set operation properties like associativity and distributivity to guide verification. **Outcome:** After computation, both sides of each equation should yield identical sets, illustrating the associative property of union and intersection. ---
Transcribed Image Text:The text comprises a mathematical exercise about set theory. Below is the transcription tailored for an educational website setting: --- **Exercise: Verification of Set Equations** Consider the following sets: - \( A = \{1, 2, 5, 7, 9\} \) - \( B = \{1, 3, 4, 7, 8\} \) - \( C = \{3, 4, 6, 8\} \) **Objective:** Verify each equation using direct computation. a. Verify the equation: \( A \cup (B \cup C) = (A \cup B) \cup C \) b. Verify the equation: \( A \cap (B \cap C) = (A \cap B) \cap C \) **Instructions:** 1. **Union (\( \cup \)) and Intersection (\( \cap \)) Operations:** - **Union (\( \cup \))**: The set containing all distinct elements present in any of the sets involved. - **Intersection (\( \cap \))**: The set containing all elements common to all sets involved. 2. **Verify Each Side of the Equations:** - Compute the left-hand side and right-hand side of each equation and check for equality. **Additional Notes:** - Detail each step carefully to ensure accuracy. - Use set operation properties like associativity and distributivity to guide verification. **Outcome:** After computation, both sides of each equation should yield identical sets, illustrating the associative property of union and intersection. ---
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Given,A={1,2,5,7,9}B={1,3,4,7,8}C={3,4,6,8}

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