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

The sets A and B correctly represent functions.

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.