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?



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.


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