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Questions and Answers
What is a relation in a set A defined as?
What is a relation in a set A defined as?
- A subset of A (correct)
- A superset of A
- A superset of B
- A subset of B
Which property must a relation have to be considered an equivalence relation?
Which property must a relation have to be considered an equivalence relation?
- Reflexive, asymmetric, and transitive
- Reflexive, symmetric, and transitive (correct)
- Reflexive, transitive, and antisymmetric
- Symmetric, transitive, and antisymmetric
In Example 2, why is the relation R considered reflexive?
In Example 2, why is the relation R considered reflexive?
- Every element in T is congruent to at least one other element
- Every element in T is not congruent to any other element
- Every element in T is congruent to itself (correct)
- Every element in T is not congruent to itself
Which example represents an empty relation in a set A?
Which example represents an empty relation in a set A?
Why is the relation R in Example 3 not reflexive?
Why is the relation R in Example 3 not reflexive?
What does a universal relation in a set A indicate?
What does a universal relation in a set A indicate?
In Example 3, why is the relation R considered symmetric?
In Example 3, why is the relation R considered symmetric?
Which term refers to relations where no elements are related to any other element?
Which term refers to relations where no elements are related to any other element?
What is the relation R = {(a, b) : |a - b| ≥ 0} named as?
What is the relation R = {(a, b) : |a - b| ≥ 0} named as?
Why is the relation R in Example 3 not transitive?
Why is the relation R in Example 3 not transitive?
In a universal relation in set A, what is the relationship between elements?
In a universal relation in set A, what is the relationship between elements?
In Example 4, why is the relation R considered reflexive?
In Example 4, why is the relation R considered reflexive?
Which property does the relation R in the set Z of integers lack?
Which property does the relation R in the set Z of integers lack?
Why is it stated that the relation R in the set Z is an equivalence relation?
Why is it stated that the relation R in the set Z is an equivalence relation?
What does the statement 'a – c = (a – b) + (b – c) is even' imply?
What does the statement 'a – c = (a – b) + (b – c) is even' imply?
Which integers are related to zero in the relation R in the set Z?
Which integers are related to zero in the relation R in the set Z?
What does the subset E consisting of all even integers represent?
What does the subset E consisting of all even integers represent?
Why are no elements of E related to elements of O in the set Z?
Why are no elements of E related to elements of O in the set Z?
Which of the following best defines an onto function?
Which of the following best defines an onto function?
In Example 7, why is the function $f: A \to N$ considered one-one?
In Example 7, why is the function $f: A \to N$ considered one-one?
Why is the function $f: N \to N$, given by $f(x) = 2x$, considered not onto?
Why is the function $f: N \to N$, given by $f(x) = 2x$, considered not onto?
In the given examples, which function is both one-one and onto?
In the given examples, which function is both one-one and onto?
What is the defining characteristic of a bijective function?
What is the defining characteristic of a bijective function?
Why is the function $f: R \to R$, given by $f(x) = 2x$, considered onto?
Why is the function $f: R \to R$, given by $f(x) = 2x$, considered onto?
Which of the following functions is both injective and surjective?
Which of the following functions is both injective and surjective?
Which function is proven to be neither one-one nor onto?
Which function is proven to be neither one-one nor onto?
Which function is shown to be one-one?
Which function is shown to be one-one?
In which case does a function from A to B exhibit a bijective relationship?
In which case does a function from A to B exhibit a bijective relationship?
Which function from N to N is proven to be neither injective nor surjective?
Which function from N to N is proven to be neither injective nor surjective?
Which function can be concluded as having a domain and codomain both in real numbers?
Which function can be concluded as having a domain and codomain both in real numbers?
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