Let X = { 1, 2, 3} and Y= {4, 5}. Find whether the following subsets of `X xx Y` are functions from X to Y or not.
(i) f = {(1, 4), (1, 5), (2, 4), (3, 5)} (ii) g = {(1, 4), (2, 4), (3, 4)}
(iii) h = {(1, 4), (2, 5), (3, 5) } (iv) k = {(1, 4), (2, 5)}

Answer

N/a

Explanation

Given that, X = { 1, 2, 3} and Y= {4, 5}
`X xx Y` = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}
(i) f = {(1, 4), (1, 5), (2, 4), (3, 5)}
f is not a function because f has not unique image.
(ii) g = {(1, 4), (2, 4), (3, 4)}
Since, g is a function as each element of the comain has unique image.
(iii) h = {(1, 4), (2, 5), (3, 5) }
It is clear that h is a function.
(iv) k = {(1, 4), (2, 5)}
k is not a function as 3 has not any image under the mapping.