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What is the mathematical definition of a relation R from a set A to a set B?
What is the mathematical definition of a relation R from a set A to a set B?
- A relation is the intersection of sets A and B
- A relation is the union of sets A and B
- A relation is a subset of set A
- A relation is a subset of the cartesian product A × B (correct)
If no element of set A is related to any other element of set A, what is the name given to this type of relation?
If no element of set A is related to any other element of set A, what is the name given to this type of relation?
- Invertible Relation
- Functional Relation
- Universal Relation
- Trivial Relation (correct)
Which of the following statements is true about the empty relation in a set A?
Which of the following statements is true about the empty relation in a set A?
- The empty relation is a non-empty subset of A × A
- The empty relation is denoted by R = A × A
- No element in set A is related to any other element in set A (correct)
- Every element in set A is related to every other element in set A
What does it mean if a relation R from a set A to a set B is called the universal relation?
What does it mean if a relation R from a set A to a set B is called the universal relation?
If a relation R from a set A to a set B is not empty but not universal either, what type of relation does it represent?
If a relation R from a set A to a set B is not empty but not universal either, what type of relation does it represent?
What type of relation is a relation R in a set A if it is reflexive, symmetric, and transitive?
What type of relation is a relation R in a set A if it is reflexive, symmetric, and transitive?
Given a function f : X → Y, what makes f a one-to-one function?
Given a function f : X → Y, what makes f a one-to-one function?
What defines a function f : X → Y as onto?
What defines a function f : X → Y as onto?
In the context of functions, what does it mean for a function to be invertible?
In the context of functions, what does it mean for a function to be invertible?
What characterizes a binary operation ∗ on a set A?
What characterizes a binary operation ∗ on a set A?
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