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Questions and Answers
What is the total number of elements in the set A = {1, 2, {1, 2, 3}} ?
What is the total number of elements in the set A = {1, 2, {1, 2, 3}} ?
3
What is the cardinality of the set ({1, 2, 3, 4})?
What is the cardinality of the set ({1, 2, 3, 4})?
4
A relation is a set of ordered pairs.
A relation is a set of ordered pairs.
True (A)
A function is a set of ordered pairs, where no two pairs have the same first element.
A function is a set of ordered pairs, where no two pairs have the same first element.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is reflexive.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is reflexive.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is symmetric.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is symmetric.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is transitive.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is transitive.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is an equivalence relation.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} is an equivalence relation.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} has 4 equivalence classes.
The relation R = {(1, 1), (1, 2), (2, 1), (2, 2)} has 4 equivalence classes.
What is the value of n(A) = 5 if we know that n(A) represents the total number of natural numbers?
What is the value of n(A) = 5 if we know that n(A) represents the total number of natural numbers?
Flashcards
Relation on a set
Relation on a set
A set of ordered pairs from a set to itself.
Transitive Relation
Transitive Relation
If (a, b) and (b, c) are in the relation, then (a, c) must also be in the relation.
Symmetric Relation
Symmetric Relation
If (a, b) is in the relation, then (b, a) must also be in the relation.
Reflexive Relation
Reflexive Relation
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Equivalence Relation
Equivalence Relation
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Total Relations on a Set
Total Relations on a Set
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Set A
Set A
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Ordered Pair
Ordered Pair
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Example of a relation
Example of a relation
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Reflexive relations on set A
Reflexive relations on set A
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Study Notes
Relations & Functions
- Set A: {1, 2, 3, 4}
- Total Relations: 2n(A) * n(A)
- Reflexive Relations: Contain (a, a) for all a ∈ A
- Symmetric Relations: If (a, b) ∈ R, then (b, a) ∈ R
- Transitive Relations: If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R
- Equivalence Relations: Reflexive, Symmetric, and Transitive
- Cardinal Number of A: n(A)
- Maximal Number of Relations: 2n(A)2
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