# Natural Deduction to Derive Conclusion of Argument

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DIRECTIONS FOR TRANSLATIONS

Translate the following statements into symbolic form. Use the letters O, C, M, P, R, N, and L as needed. Use (> for horseshoe) (* for dot)(v wedge)(=tripple bar)(~tilde)

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1. Nikon will introduce a new lens but not both Minolta will extend its warranty and Olympus will introduce a smaller model.

2. Pentax will promote its auto flash provided that either Cannon advertises its auto focus or Ricoh increases sales.

3. Either Nikon's introducing a new lens or Leica's modernizing its factory is a sufficient condition for Ricoh to increase sales.

4. Ricoh will increase sales; however, if Leica modernizes its factory, then Pentax's promoting its auto flash is a sufficient and necessary condition for Cannon to advertise its auto focus.

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DIRECTIONS FOR THE TRUTH TABLES

Use natural deduction to derive the conclusion of each argument. Do not use conditional proof or indirect proof!

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5.

1. B v ~A

2. ~B v C

3. C > (A * D) /A=C

6.

1. ~A > (~B > C)

2. B > A

3. ~C / A

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#### Solution Preview

Please see attached file.

DIRECTIONS FOR TRANSLATIONS Translate the following statements into symbolic form. Use the letters O, C, M, P, R, N, and L as needed. Use (> for horseshoe) (* for dot)(v wedge)(=tripple bar)(~tilde)

1. Nikon will introduce a new lens but not both Minolta will extend its warranty and Olympus will introduce a smaller model.

2. Pentax will promote its auto flash provided that either Cannon advertises its auto focus or Ricoh increases sales.

3. Either Nikon's introducing a new lens or Leica's modernizing its factory is a sufficient condition for Ricoh to increase sales.

4. Ricoh will increase sales; however, if Leica modernizes its factory, then Pentax's promoting its auto flash is a sufficient and necessary condition for Cannon to advertise its auto focus.

For all of the above, mark up your paper! Break each compound sentence down to its simple, or atomic, sentences. The simple sentence is the one with no connective whatsoever. Group your major terms and ...

#### Solution Summary

The solution is a comprehensive guide to philosophy students in using syllogisms and natural deduction to derive the conclusion of each argument (see problem). Step by step, it will ease the frustration of students having trouble with natural deduction and syllogism as well as creation of truth tables in philosophy by example.