Convert the following arguments into a formal statements, e.g., define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been applied correctly.

Please include what needs to be proven, define the variables, write each line in complete sentences, justify each line, and make a complete statement when your proof is completed.

- Curly, Moe, and Larry are stooges. Curly did his homework. Therefore, a stooge did his homework.

- Curly and Moe are stooges. Therefore, Curly is a stooge.

- All numbers that are divisible by two are even. 17 is not divisible by two. Therefore 17 is not even.

- If b² > 4ac then there are two real roots of ax² + bx + c = 0 that are given by -bb2-4ac2a . Therefore x²+5x+1 = 0 has two real roots.

- If a is any real number, then x² + a² = 0 does not have any real solution. Therefore, there is no real solution to x²+4 = 0.