Question

Which of the following statements best describes the relationship of a relation and a function? Select all that apply. A relation is always a function. A function is always a relation. A function is a relation, if and only if, the x-values do not repeat in a given set. A relation is a function, if and only if, the x- values do not repeat in a given set. A function is never a relation. A relation is never a function.

Answer 1

A relation is a function, if and only if, the x- values do not repeat in a given set.

Answer 2

The statement that best describes the relationship of a relation and a function is:

• A function is always a relation.
• A relation is a function, if and only if, the x- values do not repeat in a given set.

Explanation:

Relation--

Let A and B be two set then a relation from set A to set B is the collection of the ordered pairs of the type:

(a,b) where a belongs to A and b belongs to B.

Function--

A function from set A to set B is the mapping in which each element of set A is mapped to a single element of B.

Hence, we may say that a function is always a relation but a relation need not always be a function.

For a relation being a function we may assure that each element must have a single image.

i.e. there may not exist any ordered pair of type:

(x,y) and (x,y')