In the question one statement is given, followed by two conclusions, I and II. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statement.
Statement: A function is a relation between a set of input elements and a set of possible output elements where each input is related to exactly one output.
Conclusion I : Every input element is related to every output element.
Conclusion II: Every input element is related to one element of output.

Statement: A function is a relation between a set of input elements and a set of possible output elements where each input is related to exactly one output.

This means that each input has only one corresponding output.

Conclusion I: Every input element is related to every output element.

This does not follow because the statement mentions that each input is related to exactly one output, not every output.

Conclusion II: Every input element is related to one element of output.

This follows because the statement says that each input is related to exactly one output.

Thus, correct option is (b).