Choose one of the proofs below and use one of the Indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument

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Choose one of the proofs below and use one of the Indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. Your proof may utilize any of the Rules of Inference or Equivalence Rules given in Chapter 8.

1. F → (O • B), S ↔ ~B, , W ↔ ~S, therefore F → W
2. B → (F ? ~R), (I ? P) → ~F, P, therefore B → ~R
3. ~P ↔ Q, ~(Q ? R), (P • ~R) → S, therefore S
4. S → T therefore (U ? S) → (U ? T)
5. X → Y therefore (Y ? X) → Y

In mathematics, it is very common for there to be multiple ways to solve a given problem; the same can be said of logic. There are often a variety of ways to perform a natural deduction. 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?

Journals are private and between you and the instructor only. Approach these activities as (a) an opportunity to practice and apply what you learn each week based on the assigned readings and activities, and (b) an opportunity to ask questions of your instructor regarding any areas you may need additional support with. The journal entries in this course are graded separately. Guidelines for Submission: Submit journal assignments as Word documents with double spacing, 12-point Times New Roman font, and one-inch margins.