Please type and please read the whole question. This is similar to some questions on here but they are not the same.

Below are basic arguments in English. Choose one argument and translate the argument into the symbolism of Predicate Logic. Refer to the translation chart on page 481 of your text for help translating. Then, Use one of the Indirect proof techniques combined with Rules of Inference and Equivalence from Chapter 8 to demonstrate the validity of the argument.

Next, 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 (ie. a proof that doesnt rely on making assumptions as CP and RAA do)?

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

Arguments:

There are rights that cannot be waived. But alienable rights can be waived. It follows that some rights are inalienable. (Rx: x is a right; Wx: x can be waived; Ax: x is an alienable right)

All contingent beings are causally dependent. No necessary beings are causally dependent. Every physical entity is contingent. All atoms are physical entities. We may conclude that no atom is a necessary being. (Cx: x is a contingent being; Dx: x is causally dependent; Nx x is a necessary being; Px: x is a physical entity; Ax: X is an atom)

There is an entity that is more powerful than all entities. Therefore, at least one entity is more powerful than itself. (Mxy: x is more powerful than y)

All brain processes are physical processes. No mental processes are tangible. Therefore, every brain process that is a mental process is also an intangible process. (Bx: x is a brain process; Px: x is a physical process; Mx: x is a mental process; Tx: x is tangible.)

Thank you!