Question Bank: Relations and Functions

What is a relation R from set A to set B?

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

Which type of relation means every element in set A is related to every element in set A?

What does it mean for a relation R to be reflexive?

Which of the following is a property of equivalence relations?

If R is a relation such that (1, 2) ∈ R and (2, 1) ∈ R, which property does R exhibit?

Which statement about functions as relations is true?

How do sets A = {1, 2} and B = {3, 4} relate in a function?

What describes a transitive relation?

Which of the following represents a universal relation for the set A = {1, 2}?

Identify a characteristic that all equivalence relations must have.

If R is a relation from A to B and it is defined by R = {(x, y) | x is greater than y}, which relationship property does R exhibit?

In what scenario would a function not be defined?

Which of the following is a correct statement about relations?

What defines an empty relation in a set A?

Which relation is characterized by every element being related to itself?

In which relation does (a, b) imply (b, a)?

What is the relation called if it satisfies both reflexivity and symmetry but not transitivity?

Which property must a relation have to be classified as an equivalence relation?

Which of the following is an example of a universal relation?

If A = {x ∈ R : x < 5}, what kind of relation does R = {(x, y) : x - y < 0} represent?

Which of the following examples depicts a reflexive relation?

If R is a symmetric relation, what can be implied if (a, b) belongs to R?

What is an equivalence class [a] for a given element a in the equivalence relation R?

Which relation type is represented by (a, b) in A where x + y > 4?

Which of the following statements about equivalence relations is false?

If f(x) = 2x + 1 and g(x) = x^2, what is gof(2)?

What is the composition fog(x) if f(x) = 3x - 4 and g(x) = x + 5?

For functions f(x) = x + 3 and g(x) = 2x, what is the expression for gof(x)?

If f(x) = cos(x) and g(x) = 3x^2, then what is fog(0)?

Given f(x) = x^2 and g(x) = x + 5. What is gof(3)?

If f(x) = 2x and g(x) = x - 1, find fog(4).

For f(x) = 1/x and g(x) = x + 2, find gof(x) for x > 0.

If f(x) = 2x - 1 and g(x) = x^2, determine if gof is equal to fog.

Determine f(g(1)) if f(x) = x + 5 and g(x) = 3x - 2.

If f(x) = x/x+1 and g(x) = 2x, find the gof(4).

Which of the following is a property of an injective function?

What is the definition of a surjective function?

If a function is both injective and surjective, it is called what?

Which function is an example of a many-one function?

In which scenario is a function not considered onto?

Which of the following functions is a bijection?

Which of the following graphs depicts a function that is injective?

What is the range of the function f(x) = 2x for x ∈ N?

Which function is not one-one?

If f: R → R is defined by f(x) = x + 5, what is f(0)?

Which of the following statements is true regarding the function f(x) = 1/x?

For which function is the output not limited to positive values?

Which statement is true for a constant function?

If f(x) = 2x and g(x) = x^2, what is (f∘g)(2)?

Which of the following is an example of a function that is neither injective nor surjective?