anonymous
  • anonymous
Prove: A is a subset of B iff A-B= empty set
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
hey, how's it going?
anonymous
  • anonymous
hi there I am just cracking my head on this proof
anonymous
  • anonymous
I started but am stuck

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anonymous
  • anonymous
hmm, i'm not the best at formal proofs, but let's see
anonymous
  • anonymous
A is a subset of B means that every element of A is an element of B
anonymous
  • anonymous
yes
anonymous
  • anonymous
then A-B is the set of elements in A that don't belong to set B
anonymous
  • anonymous
yeah
anonymous
  • anonymous
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
anonymous
  • anonymous
that's a little confusing can you explain that again?
anonymous
  • anonymous
we want to know what A-B is, or the set of elements in A that don't belong to B
anonymous
  • anonymous
we started with A is a subset of B, which means that every element of A is an element of B
anonymous
  • anonymous
right I understand that so far
anonymous
  • anonymous
so for any element in A, we know that it is also in B
anonymous
  • anonymous
so for any element in A, we know that it is also in B
anonymous
  • anonymous
yes
anonymous
  • anonymous
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.
anonymous
  • anonymous
hey, you still there?

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