Consider the following proposition: For each integer a, a = 2 (mod 8) if and only if (a^2 + 4a) = 4 (mod 8).

(a) Write the proposition as the conjunction of two conditional statements.

(b) Determine if the two conditional statements in Part (a) are true or false. If a conditional statement is true, write a proof, and if it is false, provide a counterexample.

(c) Is the given proposition true or false? Explain.