Quiz on Relations and Functions

What is defined as an arbitrary subset of A × B in mathematics?

• Mapping

• Function

• Relation

• Set

Which of the following is an example of an empty relation?

• R = {(a, b) : a is sister of b}

• R = {(a, b) : a - b = 10}

• R = {(a, b) : a + b = 0}

• R = {(a, b) : a is brother of b}

What type of relation is defined if (a, a) ∈ R for every a ∈ A?

• Reflexive

• Universal

• Transitive

• Symmetric

Which of the following relations is symmetric?

• R = {(1, 2), (2, 3)}

• R = {(1, 2), (2, 1)}

• R = {(1, 1), (2, 2)}

• R = {(1, 2), (3, 4)}

What is the definition of a universal relation?

• R = {(a, b) : a = b}

• R = {(a, b) : a is not related to b}

• R = A × A

• R = φ ⊂ A × A

Which of the following is an equivalence relation?

• R = {(x, y) : x is congruent to y mod 2}

• R = {(x, y) : x is greater than y}

• R = {(x, y) : x + y = 0}

• R = {(x, y) : x < y}

What is the range of a function?

• The set of all ordered pairs

• The set of all possible outputs

• The set of all possible inputs

• The set of all relations

Which of the following functions is one-one?

• f(x) = sin(x)

• f(x) = x + 1

• f(x) = x^2

• f(x) = 2x + 3

What is the definition of a bijective function?

• Onto only

• Neither one-one nor onto

• One-one only

• One-one and onto

Which of the following is a characteristic of finite sets?

• A function can be onto but not one-one

• A function can be one-one but not onto

• An onto function is necessarily one-one

• A one-one function is necessarily onto