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4) Prove that SUT=SnT for all sets S and T

4) Prove that SUT=SnT for all sets S and T

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Problem 4:** Prove that \( S \setminus (S \cup T) = S \setminus T \) for all sets \( S \) and \( T \). --- **Explanation:** This mathematical statement involves set theory, focusing on set subtraction, also known as set difference. The problem asks to prove the equality of two set expressions. - **Left Side**: \( S \setminus (S \cup T) \) means we take the set \( S \) and remove all elements that are in the union of \( S \) and \( T \). Since the union \( S \cup T \) includes all elements of \( S \), this will effectively remove all elements of \( S \), resulting in an empty set unless \( T \) also removes elements not in \( S \). - **Right Side**: \( S \setminus T \) indicates taking the set \( S \) and removing elements that are in \( T \). This problem is a fundamental application of understanding how sets interact with operations like union and subtraction.
Transcribed Image Text:**Problem 4:** Prove that \( S \setminus (S \cup T) = S \setminus T \) for all sets \( S \) and \( T \). --- **Explanation:** This mathematical statement involves set theory, focusing on set subtraction, also known as set difference. The problem asks to prove the equality of two set expressions. - **Left Side**: \( S \setminus (S \cup T) \) means we take the set \( S \) and remove all elements that are in the union of \( S \) and \( T \). Since the union \( S \cup T \) includes all elements of \( S \), this will effectively remove all elements of \( S \), resulting in an empty set unless \( T \) also removes elements not in \( S \). - **Right Side**: \( S \setminus T \) indicates taking the set \( S \) and removing elements that are in \( T \). This problem is a fundamental application of understanding how sets interact with operations like union and subtraction.
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