Polynomials are mathematical functions of the form: f(x) = a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0 where a_n, a_{n-1}, …, a_1, a_0 are constants and n is a non-negative integer. Special polynomials are those that have particular properties or are used to solve specific problems. Some examples of special polynomials…
Onto and one-to-one are both terms used to describe functions in mathematics. An onto function (also called a surjective function) is a function in which every element in the range is mapped to by at least one element in the domain. In other words, for every element y in the range, there exists at least…
In mathematics, the range of a function is the set of all possible output values that the function can produce when it is applied to the elements of its domain. It is sometimes called the image of the function. The range is a subset of the codomain, which is the set of all possible output…
In mathematics, the codomain of a function is the set of all possible values that the function can output or map to. It is the set of all possible values of the dependent variable of the function, which corresponds to the output of the function given a particular input. For example, if we have a…
Functions are mathematical objects that take one or more inputs and produce an output based on some rule or relationship between the inputs and the output. In other words, functions can be thought of as mappings that associate each input with a corresponding output. For example, consider the function f(x) = 2x + 1. This…
In mathematics, a relation is a set of ordered pairs that relate objects in some way. A function is a special type of relation where each input (also called the domain) has exactly one output (also called the range). More formally, a function f is a relation from a set A to a set B,…
In mathematics, an equivalence relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity. An equivalence relation is used to partition a set into disjoint subsets called equivalence classes. More specifically, let R be a relation on a set A. Then, R is an equivalence relation if and only if it satisfies the…
In mathematics, a relation is a set of ordered pairs that relate elements of two sets. The domain and codomain are important concepts when it comes to understanding relations. The domain of a relation is the set of all first elements of the ordered pairs in the relation. In other words, it is the set…
The Cartesian product of two finite sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B. Symbolically, A × B = {(a, b) | a ∈ A and b ∈ B} For example,…
The main difference between De Morgan’s Law for Union and De Morgan’s Law for Intersection is the way they apply to sets. De Morgan’s Law for Union states that the complement of the union of two or more sets is equal to the intersection of the complements of those sets, while De Morgan’s Law for…