The symmetric difference of A and B, denoted

2022-04-03 Answered

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.
a) Find the symmetric difference o f { 1, 3 , 5 } and { 1, 2, 3 } .
b) Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it follow that
A (B C) = (A B) C?

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Answers (1)

RizerMix
Answered 2022-05-13 Author has 438 answers

Given: A={ 1, 3 , 5 } and B={ 1, 2, 3 }

 

The formula of symmetric difference of two sets:

A+B=(AB)-(AB)

Thus, 

{1,3,5}{1,2,3}={1,2,3,5} and

{1,3,5}{1,2,3}={1,3}

 

{1,3,5}+{1,2,3}={1,2,3,5}-{1,3}={2,5}

Hence, A-B={x|xA but xB}

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