Final answer:
The statement is false because even and odd functions have different symmetry properties that cannot be satisfied simultaneously by any non-zero function.
Step-by-step explanation:
The statement "A function can be both even and odd" is false. An even function satisfies the condition y(x) = y(-x), which means it is symmetric about the y-axis. On the other hand, an odd function meets the condition y(x) = -y(-x), indicating symmetry about the origin after a 180-degree rotation. For a function to be both even and odd, it would have to equal its negative over all domains, which is only true for the zero function. Therefore, except for this trivial case, functions cannot be both even and odd due to the contradicting symmetry properties.