Solution Found!
The symmetric difference of A And B, denoted by A ? B, is
Chapter 1, Problem 43E(choose chapter or problem)
Problem 43E
The symmetric difference of A And B, denoted by A ⊕ B, is the set containing those elements in either A or B, but not in both A And B.
If A, B, C. and D are sets, does it follow that (A ⊕) ⊕ (C ⊕ D) = ( A ⊕ D) ⊕ (B ⊕ C)?
Questions & Answers
QUESTION:
Problem 43E
The symmetric difference of A And B, denoted by A ⊕ B, is the set containing those elements in either A or B, but not in both A And B.
If A, B, C. and D are sets, does it follow that (A ⊕) ⊕ (C ⊕ D) = ( A ⊕ D) ⊕ (B ⊕ C)?
ANSWER:
Answer:
Step 1:
In this problem we need to show that , where A , B , C and D are sets.
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SYMMETRIC DIFFERENCE: The symmetric difference of two sets A and B is the set containing all those elements which belongs either to A or to B but not to both , and it is denoted by
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In this problem we use membership table to check the given statement.
=
If A = B = 1, then = 1 - 1= 0.
If A = 1 , B = 0, then = 1 - 0= 1.
If A = 0 , B = 1, then = 1 - 0= 1.
If A = B = 0, then = 0 - 0= 0.
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