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. f 1 = {(1, 1), (2, 11), (3, 1), (4, 15)} ii. f 2 = {(1, 1), (2, 7), (3, 5)} iii. f 3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

Question

Philoid · Accepted Answer

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.

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)}

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)}