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

Answer 1

Answer:

The sets A and B correctly represent functions.

Step-by-step explanation:

A set of ordered pairs in the format $(x,y)$ represents a function if for each value of x, there is only one value for y.

The first set is A

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

For each value of x, there is only one value of y. So this set of relations correctly represents a function.

The second set is B

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

Again, for each value of x, there is only one value of y. So this set of relations correctly represents a function.

The third set is C

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

We have three values of y for x = 0. So this set does not represent a function.

Answer 2

Answer with Explanation:

A relation in a set is said to be function, if every first element of an ordered pair in a set is  related with unique element of second element.

No,two distinct second element of an ordered pair,has same first element.

For,example ,{(1,2),(1,3),(4,5)}, is not a function but it is a relation.

In Ordered pair, (x,y)

x=First Element

y= Second Element

→In Set A

First Element              Second Element

 1                                           3

 -1                                          5

 6                                          4

Every First  element of set A has unique second element. So, it is a function.

→In Set B

First Element              Second Element

 2                                          0

 4                                          6

 -4                                          5

   0                                          0

Every First  element of set B has unique second element and no two distinct Second element of set B,has same first element. So, it is a function.

→In Set C

First Element              Second Element

 1                                           1

 0                                          2

 0                                          3

 -3                                          5

As, two same first element of set C has distinct second element. So, it is not a function.

Set A and Set B , are functions,but Set C is not.