Proof of A △ (B △ C) = (A △ B) △ C (Associativity of the Symmetric Difference)

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In this exercise we will proof the associativity of the symmetric difference of three sets.

⏰ Timeline
00:00 Exercise
00:26 Symmetric difference
01:09 Simplifying
03:51 Symmetric difference of the right side
04:14 Simplifying
04:46 Comparing
05:15 Conclusion

🔢 Equation to proof
A △ (B △ C) = (A △ B) △ C

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Creative Commons — Attribution 3.0 Unported — CC BY 3.0
  1. Florian Ludewig
  2. A △ (B △ C) = (A △ B) △ C
  3. symmetric difference
  4. set theory
  5. proof of equality
  6. equality of sets proof
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Комментарии
Автор

Thanks for the proof.
The second line from the bottom, should contain xeC instead of xeB. Same for the x not element of B statement.

MrMuffinwomen
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3:46 "At this point we can't really simplify this term anymore"

I felt that.

loodi
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Thanks for the help. Got stuck on this one while doing the math assignment.

rajatshukla
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could you prove it but using set operationes and the definition of symmetric difference?

gurumitar
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I proved this using the difinition of the symmetric difference that has complements in it. with simplifying I concluded that the two statements are equal, can this be right?

Mapsycholek
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So parantheses are reduntant when Logical OR is used? like you said in 3:12

so basically:
((B NOT C) OR ( C NOT B))
Can I just say (B NOT C OR C NOT B)

rahmatazam
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im a little confused why you needed de morgan’s law. If it is not in the symmetric difference of b and c then it would have to either not in b or c or be in b and c right?

joshualiu
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Thanks a lot, you saved my life!!! :D

socco
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(A U B) ∆ C me puede explicar por favor este tipo de ejercicio

hubertleemartinezmartinez
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Thank you very much, professor, you helped me a lot

SalmaSalma-osqe
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I can't understand what you written

ktmandotherrider
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the third line from the end, didnt you forget 'the 'not'' at some point

chandrenselly
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I can barely hear you voice. turn up the music more so I can't hear you no more.

shtshot