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.

(a) f₁ = {(1, 1), (2, 11), (3, 1), (4, 15)}
(b) f₂ = {(1, 1), (2, 7), (3, 5)}
(c) f₃ = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

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Solution

(a) Given:
f₁ = {(1, 1), (2, 11), (3, 1), (4, 15)}
f₁ is a function from X to Y.

(b) Given:
f₂ = {(1, 1), (2, 7), (3, 5)}
f₂is not a function from X to Y because 2 ∈ X has no image in Y.

(c) Given:
f₃ = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}
f₃ is not a function from X to Y because 2 ∈ X has two images, 9 and 11, in Y.

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Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
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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. (a) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)} (b) f2 = {(1, 1), (2, 7), (3, 5)} (c) 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.

(a) f₁ = {(1, 1), (2, 11), (3, 1), (4, 15)}
(b) f₂ = {(1, 1), (2, 7), (3, 5)}
(c) f₃ = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}