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Questions and Answers
What is the relationship between a relation and a Cartesian product?
What is the relationship between a relation and a Cartesian product?
- A relation and a Cartesian product are always equal.
- A relation is a superset of the Cartesian product.
- A relation and a Cartesian product have no connection.
- A relation is a subset of the Cartesian product. (correct)
Which of the following characteristics define a reflexive relation?
Which of the following characteristics define a reflexive relation?
- The relation includes all possible pairs from the Cartesian product.
- Every element is related to itself. (correct)
- If a is related to b, then b is related to a.
- If a is related to b and b is related to c, then a is related to c.
What is the domain of a relation, in terms of ordered pairs (x, y)?
What is the domain of a relation, in terms of ordered pairs (x, y)?
- The set of all possible y values.
- The set of all ordered pairs in the relation.
- The set of all possible x values. (correct)
- The set of all possible relations between x and y.
Which of the following is an example of a symmetric relation?
Which of the following is an example of a symmetric relation?
What is the difference between a universal relation and an empty relation?
What is the difference between a universal relation and an empty relation?
Flashcards
Relation
Relation
A connection between sets of elements, similar to family relationships.
Domain and Range
Domain and Range
Domain is the x value; Range is the y value in a function.
Empty Relation
Empty Relation
A relation with no elements or pairs.
Reflexive Relation
Reflexive Relation
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Equivalence Relation
Equivalence Relation
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Study Notes
Introduction to Relations and Functions
- Sets are a well-defined collection of objects
- A relation is a connection between sets of elements, like the relationship between family members
- We use the Cartesian product (A x B) to check the relationship between two sets A and B
- There are pairs of values within the Cartesian product
- The relation of sets A and B always forms a subset or equal to the Cartesian product (A x B)
- Relations are defined by a specific condition
- The Domain is the x value and the Range is the y value
- To calculate the result, we substitute the x value in the equation to get the y value (Range)
- The y value is then used to create a relation pair
- The Relation (R) is a subset of the Cartesian product (A x B)
Types of Relations
- Empty Relation: A relation that has no elements or pairs (R = ∅)
- Universal Relation: A relation that contains all possible pairs in the Cartesian product
- Reflexive Relation: A relation in which every element is paired with itself, like (a, a), (b, b), etc.
- Symmetric Relation: If a is related to b, then b is related to a (a, b) and (b, a) are both part of the relationship
- Transitive Relation: If a is related to b, b is related to c, then a is related to c. If (a, b) and (b, c) are in the relation, then (a, c) is also part of the relation
- Equivalence Relation: A relation that is reflexive, symmetric, and transitive
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