MHB Proof of a set union and intersection

AI Thread Summary
The discussion revolves around understanding the concepts of set union and intersection, particularly in the context of an assignment. The user presents two examples, one with a union resulting in R and an intersection of {0}, and another with a union of (0, 2) and an intersection of {1}. The professor clarifies that an intersection must contain elements common to all sets involved, while no other elements can belong to it. Participants agree that the user has correctly applied the definition of intersection, despite initial confusion about interpreting the professor's explanation. Overall, the conversation emphasizes the importance of understanding set definitions in mathematical proofs.
bargaj
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Hello!
Lately, I've been struggling with this assignment. (angle brackets represent closed interval)
Screenshot_20211116_184448(1).png


I figured out that:

a)
union = R
intersection = {0}
b)
union = (0, 2)
intersection = {1}

I asked my prof about this and she explained to me that it should be shown that if a set is an intersection of sets, then it belongs to each of those sets and, conversely, nothing else belongs to the intersection, so every other element does not belong to at least one of those sets. But I don't really know how to interpret this or where to even start. (normally, when proving the equality of two sets, I would try to prove that A⊆B and B⊆A, but I don't see how that's applicable here).

Thank you for your help!
 
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bargaj said:
angle brackets represent closed interval
Never seen this notation. Usually closed intervals are denoted by square brackets.

bargaj said:
a)
union = R
intersection = {0}
b)
union = (0, 2)
intersection = {1}
I agree.

bargaj said:
I asked my prof about this and she explained to me that it should be shown that if a set is an intersection of sets, then it belongs to each of those sets and, conversely, nothing else belongs to the intersection, so every other element does not belong to at least one of those sets.
So we reached a consensus, right?

bargaj said:
But I don't really know how to interpret this or where to even start.
You not only started, but also finished solving these problems.The professor just described the definition of intersection, which you have successfully applied, so you must have understood it.
 
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