Question

Which statement is correct about relations and functions?

Answer 1

Definition 1: A relation is any subset of a Cartesian product. For instance, a subset of $A\times B$, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first components from A and second components from B, and, in particular, a subset of $A\times A$ is called a "relation on A."

Definition 2: A function is a relation that associates each element x of a set X to a single element y of another set Y (possibly the same set). A function is uniquely represented by its graph which is the set of all ordered pairs (x, f (x)).

From these definitions you can see that every function is a relation from X to Y, but not via versa (because you can consider relation $\{1\}\times \{2,3\}$ - here for one x exist two y).

Answer: Correct choice is B.

Answer 2

All functions are relations. Option (b) is correct.

Further explanation:

Given:

The options area as follows,

(a). All relations are functions.

(b). All functions are relations.

(c). No relations are functions.

(d). No functions are relations.

Explanation:

Relation can be defined as relationship between the two sets in a ordered pairs that contains one object from each set.

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

A function is a type of relation.

The one-to-one function is a function in which every value of the range has exactly one pre-image in the domain.

One-to-one function always passes the vertical line test and the horizontal line test.

All functions are relations. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.