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Quiz: Sets
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last edited
by WJ 11 years, 1 month ago
This quiz is designed to test your knowledge of basic concepts in sets.
Discuss this quiz
(Key: correct, incorrect, partially correct.)
- Let and be sets. What does it mean if we say that is an element of ?
- is an element of and is also an element of .
- INCORRECT. This is what it means for to lie in .
- is an element of .
- INCORRECT. It is true that if lies in , then also lies in ; but it is possible to lie in without lying in .
- is an element of .
- INCORRECT. It is true that if lies in , then also lies in ; but it is possible to lie in without lying in .
- is an element of , or is an element of , or both.
- is equal to , and is an element of both.
- INCORRECT. One does not need the two sets and to be equal in order to form the union .
- is an element of , or is an element of , but not both.
- INCORRECT. If lies in both and then it still qualifies to lie in .
- is equal to some element a of plus some other element of : .
- INCORRECT. This is what it means for to lie in .
- Let and be sets. What does it mean if we say that is NOT an element of ?
- is not an element of , and is not an element of .
- Either is not an element of , or is not an element of .
- INCORRECT. This is what it means for to not be an element of .
- does not belong to both and at the same time.
- INCORRECT. This is what it means for to not be an element of .
- There is some element of which is not equal to , and there is some element of which is not equal to .
- There is some element of either or which is not equal to .
- and are the same sets, and is not an element of either.
- Let and be sets. What does it mean if we say that is an element of ?
- is an element of and is also an element of .
- is an element of .
- is an element of .
- is an element of , or is an element of , or both.
- INCORRECT. This is what it means for to lie in .
- is equal to , and is an element of both.
- INCORRECT. One does not need the two sets and to be equal in order to form the intersection .
- is an element of , or is an element of , but not both.
- INCORRECT. This is what it means for to lie in .
- is equal to some element a of plus some other element of : .
- INCORRECT. This is what it means for to lie in .
- Let and be sets. What does it mean if we say that is NOT an element of ?
- cannot belong to both and B; it may belong to , or to , or to neither, but not both.
- is not an element of , and is not an element of .
- INCORRECT. This does not cover the possibility that is an element of exactly one of or
- Every element of and every element of is different from .
- INCORRECT. This is what it means for to not be an element of .
- There is some element of which is not equal to , and there is some element of which is not equal to .
- belongs to exactly one of and .
- INCORRECT. This does not cover the possibility that belongs to neither nor .
- belongs to neither nor .
- INCORRECT. This is what it means for to not be an element of .
- and are the same sets, and is not an element of either.
- Let and be sets. What does it mean if we say that is a subset of B?
- Every element in is also an element of .
- Every element in is also an element of .
- INCORRECT. This is what it means for to be a subset of .
- Every element in is equal to every element in .
- Some element in is also an element of .
- INCORRECT. This is what it means for and to have a non-empty intersection.
- Every element in is contained in some element of .
- INCORRECT. We want the elements in to be equal to elements in , not _contained_ in them.
- Every element of is equal to some element of .
- INCORRECT. This is what it means for to be a subset of .
- is an element of .
- INCORRECT. We want the elements of to be elements of B; we don't what itself to be an element of .
- Let and be sets. What does it mean if we say that is not a subset of B?
- is a subset of .
- INCORRECT. It is possible for and to not be subsets of each other.
- is equal to .
- and are disjoint.
- INCORRECT. It is possible for and to partially intersect without being subsets of each other.
- There is an element of which does not lie in .
- Every element of does not lie in .
- INCORRECT. It is possible for and to still have common elements without being a subset of .
- There is an element of which does not lie in .
- INCORRECT. This is what it means for to not be a subset of .
- is not an element of .
- Let and be sets. What does it mean if we say that is equal to ?
- Every element in is also an element of , and every element in is also an element of .
- Every element in is equal to some element of .
- INCORRECT. This only shows that is a subset of .
- Every element in is equal to every element in .
- INCORRECT. This only shows that is a subset of .
- Some element in is equal to some element of .
- INCORRECT. This only shows that and have some non-empty intersection.
- is not contained in , and is not contained in .
- INCORRECT. If and are equal, then they are automatically contained in each other.
- is not strictly contained in , and is not strictly contained in .
- INCORRECT. It is possible for and to be unequal, and to not be strictly contained in each other.
- Every element in is equal to every element in .
- INCORRECT. This can only be true if and have at most one element.
- Let and be sets. What does it mean if we say that and are disjoint?
- There does not exist any element which belongs to both and .
- is not a subset of , and is not a subset of .
- is not equal to .
- The union of and is empty.
- There exists an element of and an element of such that is not equal to .
- There is an element of which is not in , and there is an element of which is not in .
- Let and be sets. What does it mean if we say that and are not disjoint?
- There exists an element which belongs to both and .
- Either is a subset of , or is a subset of .
- is a subset of , and is a subset of .
- is equal to .
- Every element of is equal to every element of .
- Every element of is equal to some element of , and vice versa.
- The union of and is non-empty.
- Let and be sets. What does it mean if we say that is not equal to ?
- Either there is some element of which is not in , or there is some element in which is not in , or both.
- There is some element of which is not in , and there is some element in which is not in .
- Either is a subset of , or is a subset of .
- Either is a proper subset of , or is a proper subset of .
- For every in and every , is not equal to .
- For every in there is some such that is not equal to .
- There is some in and some such that is not equal to .
- Let be the set . What does it mean if we say that is an element of ? (It turns out that is in fact the half-open interval (why?). But you did not need to know that to work out this problem.)
- is equal to for some .
- is equal to for every .
- is between and .
- is between and .
- is between and .
- is an element of .
- Let be the set . What does it mean if we say that is not an element of ?
- There exists such that is not equal to .
- For every , is not equal to .
- is not between and .
- is not between and .
- is not between and .
- is not an element of .
Score:
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Quiz: Sets
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