Question

1. on the accompanying diagram, draw a mapping of a relation from set a to set b that is not a function. explain why the relationship you drew is not a function.

set a
1 •
2 •
3 •
set b

• a
• b
• c

Explanation:

Step1: Draw the mapping

Let's map element 1 in Set A to both \( a \) and \( b \) in Set B, map 2 to \( c \), and map 3 to \( a \). (The drawing would show two arrows from 1 to \( a \) and \( b \), one arrow from 2 to \( c \), and one arrow from 3 to \( a \).)

Step2: Recall the definition of a function

A function from a set \( X \) to a set \( Y \) is a relation such that each element \( x \) in \( X \) is related to exactly one element \( y \) in \( Y \).

Step3: Analyze the drawn mapping

In our mapping, the element 1 in Set A is related to two elements (\( a \) and \( b \)) in Set B. Since a function requires each element in the domain (Set A) to be mapped to exactly one element in the codomain (Set B), this relation does not satisfy the definition of a function.

A function requires every element in the domain (Set A) to have exactly one image in the codomain (Set B). Here, the element 1 in Set A is mapped to two elements (\( a \) and \( b \)) in Set B, so this relation is not a function.

Answer:

To draw a non - function relation: Map 1 (from Set A) to both \( a \) and \( b \) (in Set B), 2 to \( c \), and 3 to \( a \).