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Questions and Answers
A relation on a set is a proper subset of the Cartesian product of the set with itself.
True
The Cartesian product of a set with itself is always a relation on the set.
False
A relation on a set is always a subset of the Cartesian product of the set with itself.
True
The Cartesian product of a set with itself is a relation on the set.
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A relation on a set can be a subset of a set other than the Cartesian product of the set with itself.
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A relation on a set is always a proper subset of the Cartesian product of the set with itself.
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The Cartesian product of a set with itself can be a relation on the set if it is a subset of itself.
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A relation on a set is a subset of the Cartesian product of a different set with itself.
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The empty set is a relation on a set if the set is empty.
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A relation on a set must contain all elements of the Cartesian product of the set with itself.
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Study Notes
Relations on a Set
- A relation on a set is a subset of the Cartesian product of the set with itself.
- The Cartesian product of a set with itself always contains a relation on the set.
Important Distinctions
- The Cartesian product of a set with itself is not always a relation on the set.
- A relation on a set is not always the Cartesian product of the set with itself.
Subset Relationship
- A relation on a set can be a subset of the Cartesian product of the set with itself, but it's not the only possibility.
- A relation on a set can also be a subset of another set, not necessarily the Cartesian product of the set with itself.
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Description
This quiz covers the properties and characteristics of relations on sets in discrete mathematics. It explores the connection between relations and the Cartesian product of a set with itself.
