Title: Quiz: Relations And Functions Quiz
Course: Set_Theory > Section: Module6

Q: What is a relation in the context of set theory?
- A set of unordered pairs
- A set of ordered pairs from two sets
- A single element from a set
- A mathematical equation
A: A set of ordered pairs from two sets

Q: Which of the following describes a function?
- A relation where each element of the domain is associated with multiple elements of the codomain
- A relation where each element of the domain is associated with exactly one element of the codomain
- A relation that has no elements
- A set of unordered pairs
A: A relation where each element of the domain is associated with exactly one element of the codomain

Q: When is a function considered injective?
- When every element in the codomain is mapped by at least one element in the domain
- When no two different elements in the domain map to the same element in the codomain
- When it has a unique output for every input
- When it can be represented as a graph
A: When no two different elements in the domain map to the same element in the codomain

Q: How can functions be represented?
- Only through equations
- Only through graphs
- Through graphs, tables, and equations
- Only through verbal descriptions
A: Through graphs, tables, and equations

Q: What does the term "codomain" refer to in a function?
- The set of all possible input values
- The set of all possible output values
- The set of ordered pairs
- The set of elements that do not belong to the function
A: The set of all possible output values

Q: Why is understanding the properties of functions important?
- It helps in memorizing mathematical definitions
- It allows for the analysis of their behavior and applications
- It is not necessary for higher mathematics
- It only applies to basic arithmetic
A: It allows for the analysis of their behavior and applications

Q: What is the Cartesian product of two sets \( A \) and \( B \)?
- A set of all possible unordered pairs
- A set of all possible ordered pairs
- A set of elements that are common to both sets
- A set that contains only the largest elements from both sets
A: A set of all possible ordered pairs

Q: Which property must a function satisfy to be classified as surjective?
- Each input must have a unique output
- Every element in the codomain must be mapped by at least one element in the domain
- It must be continuous
- It must be periodic
A: Every element in the codomain must be mapped by at least one element in the domain

Q: What does it mean for a function to be bijective?
- It is neither injective nor surjective
- It is both injective and surjective
- It has no defined output
- It is only defined for positive numbers
A: It is both injective and surjective

Q: How does a table of values help in understanding functions?
- It provides a visual representation of the function
- It lists all possible values of the function
- It displays input-output pairs clearly
- It shows only the maximum and minimum values
A: It displays input-output pairs clearly