Amanda's Chapter 5 outline
When dealing
with sets, we need to remember the definitions and theorems:
1. Set A is a subset of B if every element in A is in B.
2. Set A is a subset of A.
3. The empty set is a subset of every set.
4. Sets A and B are equal if A is a subset of B and B is a subset of A.
5. There is only one empty set.
Now to prove A is the subset of B, show if x is in A then x is in B.
One operation on sets is A intersect B; x is in A intersect B when x is in A and x is in B. Another operation is A union B; x is in A union B when x is in A or x is in B. We can have infinitely many sets, where x is in A intersect B intersect C intersect D all the way to infinity, if x is in all of the sets given. Similarly, x is in A union B union C union D all the way to infinity, if x is in at least one of the given sets. Remember that when proving union propositions, it is important to use cases where at least one has to be true for the whole proposition to be true.
One last note: x is in A complement when x is not in A.
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