Final Answer:
Relations are function, each input in the specified relations has a unique corresponding output. B) All of them.
Step-by-step explanation:
Functions are mathematical relations in which each input value corresponds to exactly one output value. In the given choices, "All of them" is the correct answer because both Choice II and Choice III describe relations that satisfy the criteria of being functions.
In mathematical terms, a relation is a function if and only if each input (independent variable) maps to exactly one output (dependent variable). "All of them" encompasses both Choice II and Choice III, making it the correct selection.
Choice II and Choice III adhere to the fundamental principle of functions, ensuring that each input has a unique corresponding output. Therefore, the relations described in both choices satisfy the conditions necessary for being functions.
In summary, to clarify, when considering mathematical relations and functions, it's essential to examine whether each input value is associated with only one output value. In this case, the correct choice is B) All of them.