Final answer:
None of the functions are injective or surjective, but (a) and (b) are partial functions while (c) is a total function.
Step-by-step explanation:
(a) f(x)= has_age Domain: people
(b) f(x)= plays_instrument Domain: children
(c) f(x)= major Domain: students (assume that there are no double majors, and single majors are also considered)
Injective: An injective function is one in which different inputs map to different outputs. In this case, none of the functions are injective because multiple people can have the same age, play the same instrument, or have the same major.
Partial: A function is partial if it does not cover the entire domain. In this case, (a) and (b) are partial functions because they only cover specific subsets of the domain (people with a certain age and children who play instruments). (c) is a total function because it covers the entire domain of students' majors.
Surjective: A function is surjective if every element in the codomain has a corresponding element in the domain. None of the functions are surjective because there are people who do not have an age, children who do not play instruments, and students who have not declared a major.