# Sets and Functions : The Symmetric Difference of Two Sets

The symmetric difference of two sets A and B, denoted by A Δ B, is defined by A Δ B = ( A - B ) U ( B - A ); it is thus the union of their differences in opposite orders. Show that A Δ ( B Δ C ) = ( A Δ B ) Δ C.

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Topology

Sets and Functions (X)

The Algebra of Sets

The Symmetric Difference of two Sets

By:- Thokchom Sarojkumar Sinha

The symmetric difference of two sets and , denoted by , is defined by ; it is thus

the union of their differences in opposite orders. Show that

Solution:- To show that

We have,

,

where

For

...

#### Solution Summary

The symmetric difference of two sets is investigated in an attached word file. The solution is well-detailed, including written notes to aid understanding and many lines of fully-displayed calculation.

Sets and Functions : The symmetric difference of two sets

The symmetric difference of two sets and , denoted by , is defined by ; it is thus the union of their differences in opposite orders.

Show that

A Δ φ = A ; A Δ A = φ