Relations on Sets in Discrete Math
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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.

<p>False</p> Signup and view all the answers

A relation on a set can be a subset of a set other than the Cartesian product of the set with itself.

<p>False</p> Signup and view all the answers

A relation on a set is always a proper subset of the Cartesian product of the set with itself.

<p>False</p> Signup and view all the answers

The Cartesian product of a set with itself can be a relation on the set if it is a subset of itself.

<p>True</p> Signup and view all the answers

A relation on a set is a subset of the Cartesian product of a different set with itself.

<p>False</p> Signup and view all the answers

The empty set is a relation on a set if the set is empty.

<p>True</p> Signup and view all the answers

A relation on a set must contain all elements of the Cartesian product of the set with itself.

<p>False</p> Signup and view all the answers

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.

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