Question

Given A = {(1, 3)(-1, 5}(6, 4)}, B = {(2, 0)(4, 6)(-4, 5)(0, 0)} and C = {(1, 1)(0, 2)(0, 3)(0, 4)(-3, 5)}, answer the following multiple choice question:
From the list of sets A, B, and C above, choose the set of relations that correctly represents a function.
Set A only
Sets A and C only
Sets A and B only

Answer 1

Sets A and B only. Set C has the x value repeating so it is not a function. 

Answer 2

Answer:

Set A and B only

Step-by-step explanation:

We are given that

A={(1,3),(-1,5),(6,4)}

B={(2,0),(4,6),(-4,5),(0,0)}

C={(1,1),(0,2),(0,3),(0,4),(-3,5)}

We are given that sets A, B and C represent the relations .

We have to choose the set of  relations that correctly represents a function

Function: It a mapping between two sets A and B. Every element of set A has unique image in set B.More than one image of an element cannot be possible or an element cannot have more than one image.Two elements or more than  two elements have same image.

In set A, each element is related with unique element.

Image of 1=3

Image of -1=5

Image of 6=4

Therefore, A represents a function.

In set B, Every element is related to a unique element.

Image of 2=0

Image of 4=6

Image of -4=5

Image of 0=0

Hence, B represents a function .

In set C

Image of 1=1

Image of 0=2

Image of 0=3

Image of 0=4

Image of -3=5

By definition of function, each element have only one image.

But 0 have more than one image.

Therefore, C does not represents  function.

Set A and B only represents a function