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 set A of relations that correctly represents a function by definition of function

Answer 2

Answer:

Only sets A and B can form a set of relations to form a function.

Step-by-step explanation:

For the given sets :

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)}

From the list of sets A, B, and C, we have to find the set of relations which represents a function.

A function f from a set X to a set Y is a relation between A  and B which satisfies two properties:

(1) every element in X is related to some element in Y, and

(2) no element in X is related to more than one element in Y

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

Let X = {1, -1, 6} and Y = {3, 5, 4}

Now, every element in X is related to some element in Y and also no element in X is related to more than one element in Y.

So, A is a set of relation and can form a function.

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

Let X = {2, 4, -4, 0} and Y = {0, 6, 5, 0}

Now, every element in X is related to some element in Y and also no element in X is related to more than one element in Y.

So, B is a set of relation and can form a function.

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

Let X = {1, 0, 0, 0, -3} and Y = {1, 2, 3, 4, 5}

Now, 0 is related to 2 in Y and also 0 is related to 4 in Y. So, one element in X is related to more than one element in Y.

So, C is not a set of relation and can't form a function.

Hence, Only sets A and B can form a set of relations to form a function.