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Questions and Answers
Explain why the relation R' is considered a universal relation.
Explain why the relation R' is considered a universal relation.
The relation R' is considered a universal relation because the difference between heights of any two students of the school is always less than 3 meters.
Define an empty relation using set notation.
Define an empty relation using set notation.
An empty relation is a relation that has no elements. In set notation, it is represented as R = φ.
How can a relation be represented in set builder notation?
How can a relation be represented in set builder notation?
A relation can be represented in set builder notation as R = {(a, b) : some condition relating a and b}.
Define a reflexive relation in terms of ordered pairs.
Define a reflexive relation in terms of ordered pairs.
Explain what it means for a relation to be symmetric.
Explain what it means for a relation to be symmetric.
Define a transitive relation using ordered pairs.
Define a transitive relation using ordered pairs.
What is the definition of an invertible function?
What is the definition of an invertible function?
How can you prove that a function is invertible?
How can you prove that a function is invertible?
In Example 17, what is the function f(x) defined as?
In Example 17, what is the function f(x) defined as?
What is the inverse of the function f(x) = 4x + 3 in Example 17?
What is the inverse of the function f(x) = 4x + 3 in Example 17?
Is the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} an equivalence relation?
Is the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} an equivalence relation?
How is the invertibility of a function shown in Example 17?
How is the invertibility of a function shown in Example 17?
Which integers are related to zero in the relation R?
Which integers are related to zero in the relation R?
Which integers are related to one in the relation R?
Which integers are related to one in the relation R?
In Example 18, why is R1 ∩ R2 reflexive if R1 and R2 are equivalence relations?
In Example 18, why is R1 ∩ R2 reflexive if R1 and R2 are equivalence relations?
What are the conditions satisfied by the sets E (even integers) and O (odd integers) in relation R?
What are the conditions satisfied by the sets E (even integers) and O (odd integers) in relation R?
What is the equivalence class containing zero denoted as in the relation R?
What is the equivalence class containing zero denoted as in the relation R?
Explain why the set E of even integers and the set O of odd integers are disjoint in relation R.
Explain why the set E of even integers and the set O of odd integers are disjoint in relation R.
Is the relation R defined by (x, y) R (u, v) if and only if xv = yu an equivalence relation?
Is the relation R defined by (x, y) R (u, v) if and only if xv = yu an equivalence relation?
For the relation R1 in X, where R1 = {(x, y) : x – y is divisible by 3}, is it equal to R2, where R2 = {(x, y): {x, y} ⊂ {1, 4, 7} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}?
For the relation R1 in X, where R1 = {(x, y) : x – y is divisible by 3}, is it equal to R2, where R2 = {(x, y): {x, y} ⊂ {1, 4, 7} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}?
What properties make a relation an equivalence relation?
What properties make a relation an equivalence relation?
How can you show that a relation is reflexive?
How can you show that a relation is reflexive?
Explain how to show symmetry in a relation.
Explain how to show symmetry in a relation.
What does it mean for a relation to be transitive?
What does it mean for a relation to be transitive?
Who was the first to use the phrase 'function of x'?
Who was the first to use the phrase 'function of x'?
Which mathematician used the notation φx for the first time in 1718?
Which mathematician used the notation φx for the first time in 1718?
Who is credited with the general adoption of symbols like f, F, φ, ψ to represent functions?
Who is credited with the general adoption of symbols like f, F, φ, ψ to represent functions?
In which year did Joseph Louis Lagrange publish his manuscripts 'Theorie des functions analytiques'?
In which year did Joseph Louis Lagrange publish his manuscripts 'Theorie des functions analytiques'?
Who gave the definition of function that was used until the set theoretic definition was developed?
Who gave the definition of function that was used until the set theoretic definition was developed?
Who developed the set theoretic definition of function after the development of set theory?
Who developed the set theoretic definition of function after the development of set theory?
