I’m trying to learn for my Mathematics class and I’m stuck. Can you help?

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)

Now, construct an alternate proof. In other words, if the proof was done using RAA, now use CP; if you used CP, now use RAA. Consider the following questions, as well, in your journal response:

• Will a direct proof work for any of these?

• Can the proof be performed more efficiently by using different equivalence rules?