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.© BrainMass Inc. brainmass.com September 23, 2018, 10:15 pm ad1c9bdddf - https://brainmass.com/math/geometry-and-topology/sets-functions-symmetric-difference-two-sets-111265
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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
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.