The input provided is not clear and complete. Can you please provide a complete question or statement for me to check and correct?
a. True - If f is a surjection and c is an element in the codomain of f, then there exists an element f⁻¹(c) in the domain of f such that f(f⁻¹(c)) = c, as required by the definition of a surjection.
b. False - A surjection guarantees that every element in the codomain has a preimage in the domain, but it does not necessarily imply that c is a preimage of f.
c. True - By the definition of a surjection, for every element c in the codomain of f, there exists an element d in the domain of f such that f(d) = c. So, f(f⁻¹(c)) = c for all c in the codomain of f.
d. False - Although a surjection guarantees that every element in the codomain has a preimage in the domain, it does not necessarily imply that f(f⁻¹(c)) = c for all c in the codomain.