Question

{(1,2), (-2,3), (1,3), (-2,2)} is what type of relation?

A. one-to-many
B. many-to-many
C. one-to-one
D. many-to-one

Answer 1

B. Many-to-many

Explanation:

We have the following ordered pairs:

• (1,2)

• (-2,3)

• (1,3)

• (-2,2)

First let's define the following concepts:

• One-to-one: A function is said to be one-to-one if every y value has exactly one x value mapped onto it.
• Many-to-one: If there are y values that have more than one x value mapped onto them.

• One-to-many: If there are x values that have more than one y value mapped onto them. (NOT A FUNCTION)

• Many-to-many: If there are x values that have more than one y value mapped onto them and at the same time, there are y values that have more than one x value mapped onto them (NOT A FUNCTION)

From all the ordered pairs, we find that the points (1,2) and (1,3) have the same x-value for diferent y-values. Also we find that the points (1,2) and (-2, 2) have different x-values for the same y-value.

Therefore, the ordered pairs DO NOT belong to a function and can be considered MANY-TO MANY.