Below are basic arguments in English. Choose one argument and translate the argument into the symbolism of predicate logic. Use one of the proof techniques from Chapter 8 to demonstrate the validity of the argument.

1. Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life).
2. Some wars are just. No war of aggression is just. Therefore, there are wars that are not wars of aggression. (Wx = x is a war, Jx = x is just, Ax = x is a war of aggression).
3. At least one instance of intentional killing is not wrong. But every murder is wrong. Hence, some instances of intentional killing are not murder. (Kx = x is an instance of intentional killing, Wx = x is wrong, Mx = x is murder)
4. Only things that have human bodies are human. No soul has a human body. Only souls survive the death of the body. Therefore, no humans survive the death of the body. (Bx = x has a human body, Hx = x is human, Sx = x is a soul, Dx = x survives the death of the body)

In your peer responses, make suggestions for an alternate proof. Consider the following questions when constructing your response:

• If the proof was done using RAA, could it be done using CP? What about vice versa?
• Will a direct proof work for any of these?
• Can the proof be performed more efficiently by using different equivalence rules?