# The symmetric difference of A and B, denoted

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

The formula of symmetric difference of two sets:

$A+B=\left(A\cup B\right)-\left(A\cap B\right)$

Thus,

$\left\{1,3,5\right\}\cup \left\{1,2,3\right\}=\left\{1,2,3,5\right\}$ and

$\left\{1,3,5\right\}\cap \left\{1,2,3\right\}=\left\{1,3\right\}$

$\left\{1,3,5\right\}+\left\{1,2,3\right\}=\left\{1,2,3,5\right\}-\left\{1,3\right\}=\left\{2,5\right\}$

Hence,