A set equation is not an identity if there are examples for the variables denoting the sets that cause the equation to be false. For example A U B = An B is not an identity because if A = {1, 2} and B = {1}, then A U B = {1, 2} and An B = {1}, which means that A U B # An B. Show that each set equation given below is not a set identity. (c) (AUB) - (ANB) = A - B Please provide correct answer. Thanks.
A set equation is not an identity if there are examples for the variables denoting the sets that cause the equation to be false. For example A U B = An B is not an identity because if A = {1, 2} and B = {1}, then A U B = {1, 2} and An B = {1}, which means that A U B # An B. Show that each set equation given below is not a set identity. (c) (AUB) - (ANB) = A - B Please provide correct answer. Thanks.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Understanding Set Equations and Identities**
A set equation is not an identity if there are examples for the variables denoting the sets that cause the equation to be false. For example, the equation \( A \cup B = A \cap B \) is not an identity. To illustrate, consider the sets \( A = \{1, 2\} \) and \( B = \{1\} \). Here, \( A \cup B = \{1, 2\} \) and \( A \cap B = \{1\} \), which demonstrates that \( A \cup B \neq A \cap B \).
**Task**
Show that the set equation given below is not a set identity.
\[ (c) \quad (A \cup B) - (A \cap B) = A - B \]
*Please provide the correct answer. Thanks.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F122c7060-cf03-40de-a20b-0aea68c956fa%2F78b9e4b4-8b5c-44e7-bc25-e8a27d166d2b%2Fy479fgi_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Set Equations and Identities**
A set equation is not an identity if there are examples for the variables denoting the sets that cause the equation to be false. For example, the equation \( A \cup B = A \cap B \) is not an identity. To illustrate, consider the sets \( A = \{1, 2\} \) and \( B = \{1\} \). Here, \( A \cup B = \{1, 2\} \) and \( A \cap B = \{1\} \), which demonstrates that \( A \cup B \neq A \cap B \).
**Task**
Show that the set equation given below is not a set identity.
\[ (c) \quad (A \cup B) - (A \cap B) = A - B \]
*Please provide the correct answer. Thanks.*
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