Podcast
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 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.
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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.
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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.
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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.
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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.
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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.
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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?
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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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Description
This quiz covers key concepts related to relations and functions, including types of relations such as reflexive, symmetric, and transitive. It also explores equivalence relations and the cardinality of sets. Test your understanding of these fundamental principles in mathematics.
