Proof Equivalence of A ⊆ B ⇔ A ∩ B = A ⇔ A ∪ B = B

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In this exercise we are going to use a circular chain of implications to proof that A subset B, A intersection B equals A and A union B equals B are equivalent statements.

⏰ Timeline
00:00 Exercise
00:11 What is to show
00:48 a implies b
02:17 b implies c
04:04 c implies a

🔢 Statements to show equivalence
A ⊆ B
A ∩ B = A
A ∪ B = B

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🎵 Music
Creative Commons — Attribution 3.0 Unported — CC BY 3.0
  1. Florian Ludewig
  2. statements
  3. equivalent statements proof
  4. proof equivalence
  5. discrete math
  6. mathe exercise
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Комментарии
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good video quality. it really healp a lot. I hope this can reach more peopl. I think the problem is that the title is too spicific to reach certain viewer base, maybe try something like "subset, iff, union, intersection, proof"

e
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I am Indian, thankyou i need this. Doubt!!

rahuljoshi
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You should put the music a tad higher, then we wouldn't be able to hear anything at all. Why do people bother ?🤔

jdmc