Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.
Are the following true?

(i) F is a relation from X to Y (ii) F is a function from X to Y. Justify your answer in following true?

Question

Philoid · Accepted Answer

X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}

and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

(i) To show: F is a relation from X to Y

First elements in F = 1, 2, 3, 4

All the first elements are in Set X

So, the first element is from set X

Second elements in F = 5, 9, 1, 11

All the second elements are in Set Y

So, the second element is from set Y

Since the first element is from set X and the second element is from set Y

Hence, F is a relation from X to Y.

(ii) To show: F is a function from X to Y

Function:

(i) all elements of the first set are associated with the elements of the second set.

(ii) An element of the first set has a unique image in the second set.

F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

Here, 2 is coming twice.

Hence, it does not have a unique (one) image.

So, it is not a function.

Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}.Are the following true?(i) F is a relation from X to Y (ii) F is a function from X to Y. Justify your answer in following true?