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Set proof

putiiik

New member
Feb 16, 2021
1
Prove that (A⊕B)∩A= A-B! Thank you!
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,518
There are various ways of proving this: using the fundamental identities of set algebra, using Euler-Venn diagrams, by definition using mutual inclusion of the left- and right-hand sides, etc. Which one is used in your course? And if it is the first method, are you familiar with the fundamental identities?
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
619
For arbitrary sets, union $A\cup B$, intersection $A\cap B$, and difference A\ B, are defined but how are you defining the "direct sum" $A\bigoplus B$ of sets?
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,518

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
619
It seems very strange to us a "+" symbol to mean a "difference".
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
9,162
It seems very strange to us a "+" symbol to mean a "difference".
It's the union of both sets except for their intersection.
As such a "+" seems appropriate.
It's just that to define it, we typically take the union of the 2 mutual differences, which is apparently why it is called symmetric difference.