functions

Following our regular procedure to solve this type of exercise, we start with the definitions. Definition: “A function f is said to be one-to-one, or an injunction, if and only if f (a) = f (b) implies that a = b for all a and b in the domain of f. A function is said […]

As usual, let’s start with relevant definitions. Definition: “If f is a function from A to B, we say that A is the domain of f and B is the codomain of f. If f (a) = b, we say that b is the image of a and a is a preimage of b. The

Let’s first review the relevant definition to solve this exercise. Definition: “If f is a function from A to B, we say that A is the domain of f and B is the codomain of f. If f (a) = b, we say that b is the image of a and a is a preimage

First, we need to know the definition of a function. Definition: “Let A and B be nonempty sets. A function f from A to B is an assignment of exactly one element of B to each element of A. We write f(a) = b if b is the unique element of B assigned by the

Let’s refresh the relevant definition we need to know to solve this exercise. “A function f from A to B is called onto, or a surjection, if and only if for every element b∈B there is an element a∈A with f (a)=b. A function f is called surjective if it is onto.” Discrete Mathematics and

In this exercise, we are asked to calculate the values of the functions floor and ceiling. Definitions: “The floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to

Let’s revisit relevant definitions that will help us solve this exercise. “If f is a function from A to B, we say that A is the domain of f and B is the codomain of f. If f (a) = b, we say that b is the image of a and a is a preimage

To solve this type of exercise, first, we need to know what is a function. “Let A and B be nonempty sets. A function f from A to B is an assignment of exactly one element of B to each element of A. We write f(a) = b if b is the unique element of

Following our normal procedure to solve this type of exercise, we start with the definitions. Definition: “A function f is said to be one-to-one, or an injunction, if and only if f (a) = f (b) implies that a = b for all a and b in the domain of f. A function is said

Following our normal procedure to solve this type of exercise, we start with the definitions. Definition: “A function f is said to be one-to-one, or an injunction, if and only if f (a) = f (b) implies that a = b for all a and b in the domain of f. A function is said