What is the difference between function and relation?

Question

What is the difference between function and relation?

Answer 1

Basically a function has only one output for each input. A relation can have more than one output (y) for each input (x). One common example is the relation in which the input (x) is a student and the output (y) is that student's teacher. Since many students have more than one teacher, that's a relation but not a function. On the other hand, the relation in which the input is a person and the output is that person's biological mother is a function, because each person has only one biological mother.

Answer 2

Hi sadaf! well a "relation" is just a relationship between sets of information. Think of all the people in one of your classes, and think of their heights. The pairing of names and heights is a relation. In relations and functions, the pairs of names and heights are "ordered", which means one comes first and the other comes second. To put it another way, we could set up this pairing so that either you give me a name, and then I give you that person's height, or else you give me a height, and I give you the names of all the people who are that tall. The set of all the starting points is called "the domain" and the set of all the ending points is called "the range." The domain is what you start with; the range is what you end up with. The domain is the x's; the range is the y's.



and



A function is a "well-behaved" relation. Just as with members of your own family, some members of the family of pairing relationships are better behaved than other. (Warning: This means that, while all functions are relations, since they pair information, not all relations are functions. Functions are a sub-classification of relations.) When we say that a function is "a well-behaved relation", we mean that, given a starting point, we know exactly where to go; given an x, we get only and exactly one y.



Hope this helps!

Answer 3

Function:

(biology)explaining why a feature survived selection

(mathematics)an abstract entity that associates an input to a corresponding output according to some rule

(# related to the utility/goal of a property

# Function (computer science), or subroutine, a portion of code within a larger program, performs a specific task

# Function object, or functor or functionoid, a concept of object-oriented programming

# Diatonic function describes a music term

# A formal event such as a party or meeting







Binary Relation

In mathematics, a binary relation (or a dyadic or 2-place relation) is an arbitrary association of elements within a set or with elements of another set.



An example is the "divides" relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p, and no other. In this relation, for instance, the prime 2 is associated with numbers that include −4, 0, 6, 10, but not 1 or 9; and the prime 3 is associated with numbers that include 0, 6, and 9, but not 4 or 13.



Binary relations are used in many branches of mathematics to model concepts like "is greater than", "is equal to", and "divides" in arithmetic, "is congruent to" in geometry, "is adjacent to" in graph theory, and many more. The concept of function is defined as a special kind of binary relation. Binary relations are also heavily used in computer science, especially within the relational model for databases.



A binary relation is the special case n = 2 of an n-ary relation, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain Xj of the relation. An n-ary relation among elements of a single set is said to be homogeneous.



In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets. This extension is needed for, among other things, modeling the concepts of "is an element of" or "is a subset of" in set theory, without running into logical inconsistencies such as Russell's paradox.





I hope you'll appreciate it........Thanks!!!☺