Q. 11

# Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}. Determine which of the following sets are functions from X to Y.i. f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}ii. f2 = {(1, 1), (2, 7), (3, 5)}iii. f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

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

i. f1 = {(1, 1), (2, 11), (3, 1), (4, 15)}

Every element of set X has an ordered pair in the relation f1 and no two ordered pairs have the same first component but different second components.

Hence, the given relation f1 is a function.

ii. f2 = {(1, 1), (2, 7), (3, 5)}

In the relation f2, the element 2 of set X does not have any image in set Y.

However, for a relation to be a function, every element of the domain should have an image.

Hence, the given relation f2 is not a function.

iii. f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

Every element of set X has an ordered pair in the relation f3. However, two ordered pairs (2, 9) and (2, 11) have the same first component but different second components.

Hence, the given relation f3 is not a function.

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