Let X = {1, 2, 3} and Y = {4, 5}.

Given, X = {1, 2, 3} and Y = {4, 5}

So, X × 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 as f(1) = 4 and f(1) = 5

Hence, pre-image ‘1’ has not unique image.

(ii) g = {(1, 4), (2, 4), (3, 4)}

It’s seen clearly that g is a function in which each element of the domain has unique image.

(iii) h = {(1,4), (2, 5), (3, 5)}

It’s seen clearly that h is a function as each pre-image with a unique image.

And, function h is many-one as h(2) = h(3) = 5

(iv) k = {(1, 4),(2, 5)}

Function k is not a function as ‘3’ has not any image under the mapping.