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anonymous

  • 5 years ago

Prove: A is a subset of B iff A-B= empty set

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  1. anonymous
    • 5 years ago
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    hey, how's it going?

  2. anonymous
    • 5 years ago
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    hi there I am just cracking my head on this proof

  3. anonymous
    • 5 years ago
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    I started but am stuck

  4. anonymous
    • 5 years ago
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    hmm, i'm not the best at formal proofs, but let's see

  5. anonymous
    • 5 years ago
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    A is a subset of B means that every element of A is an element of B

  6. anonymous
    • 5 years ago
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    yes

  7. anonymous
    • 5 years ago
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    then A-B is the set of elements in A that don't belong to set B

  8. anonymous
    • 5 years ago
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    yeah

  9. anonymous
    • 5 years ago
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    but since A is a subset of B, we know that every element of A is an element of B, so that means that there are no elements in A that don't belong to set B

  10. anonymous
    • 5 years ago
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    that's a little confusing can you explain that again?

  11. anonymous
    • 5 years ago
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    we want to know what A-B is, or the set of elements in A that don't belong to B

  12. anonymous
    • 5 years ago
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    we started with A is a subset of B, which means that every element of A is an element of B

  13. anonymous
    • 5 years ago
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    right I understand that so far

  14. anonymous
    • 5 years ago
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    so for any element in A, we know that it is also in B

  15. anonymous
    • 5 years ago
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    so for any element in A, we know that it is also in B

  16. anonymous
    • 5 years ago
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    yes

  17. anonymous
    • 5 years ago
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    so we are considering A-B, or the set of elements in A that don't belong to B. Let's assume element x is in A-B. that means that x is in A, and x is not in B. but we know that can't be true because for any element in A, we know it is in B. so x cannot exist! therefore A-B is the empty set.

  18. anonymous
    • 5 years ago
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    hey, you still there?

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spraguer (Moderator)
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