Use natural deduction to derive the conclusion of each argument.

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.
Use natural deduction to derive the conclusion of each argument. Do not use conditional proof or indirect proof!
1. B v ~A
2. ~B v C
3. C > (A * D) /A=C


1. ~A > (~B > C)
2. B > A
3. ~C / A

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...e parentheses around them as needed. What are the connectives? In line 1, you've got conjunctions, negation. Use punctuation to help you with how elements of the statement should be grouped together. In the first exercise, you're not given any, but look at how many atomic, or simple, sentences you can get out of the whole. You've got:
-Nikon introduces a new lens
-Not both Minolta does its thing and Olympus does its thing.
How are these two connected?

Here's an example of what you'd do with pen and paper:
Nikon will introduce a new lens, but not both (Minolta and Olympus).
Nikon will introduce a new lens, * ~(Minolta and Olympus).

In sentence 2, you've got Pentex doing its thing, but there is a condition for it. That condition is an either/or regarding Cannon and Ricoh. The condition is not a necessary one, so it goes in FRONT of the horse shoe.

You get told exactly where to put the condition in sentence 3, since it tells you that the either/or of Nikon or Leica is the ...