Proofs ws2
Translate into symbolic language and formally prove DV or ~DV
Use the constants prescribed for each.
1. Either God exists or evil exits. Evil exits unquestionably. Therefore, God does not exist.
[use: G, E]
2. It is not the case that Hilary is either a Republican or a Presbyterian. Therefore, she is not a Presbyterian.
[use: R, P]
3. Joe is not both a mechanic and a lawyer. He is a mechanic. So, he is not a lawyer.
[use: M, L]
4. All the people she dated were either handsome or not rich. All were rich, so, none were handsome. [use: H, R]
5. Either we interpret correctly as far as our information allows and have sufficient data, or our conclusions are untrustworthy. Given that our conclusions are trustworthy, then we have sufficient data. [use: I, S, T]
6. Translate and prove DV or ~DV
A. Either the birthrate in Canada will decline, or Canada will face an economic crisis. So it is not the case that either the birthrate in Canada won't decline or that Canada won't face an economic crisis. (Use B, E)
B. It is not true that both the price of silver is set and that people speculate on the price. People do speculate on the price of silver. Consequently, the price is not set. (Use P, S)
C. Milton didn't write both Paradise Lost and The Sun Also Rises. He did write Paradise Lost. So we know he didn't write The Sun Also Rises. (Use P, S)
7. Formally prove DV or ~DV
A. 1. ~(~A v B) v K
2. ~K
3. B v Z / .. Z
B. 1. Y . U
2. (H v T) v ~U
3. ~(Y . H) / .. G v T
C. 1. (G v N) v T
2. ~G . ~N
3. M v ~T / .. M v K
D. 1. ~(Y v K)
2. (K . P) v W
3. ~W v E /.. E
E. 1. N
2. ~Q
3. (~N . Q) v ~( A . N) /.. ~A
8. This is false: the milk is not sour but the bread is stale. Therefore?
a. Either the milk is not sour or the bread is stale
b. Either the milk is sour or the bread is not stale
c. The milk is not sour, yet the bread is stale
d. None above
9. Why is the following deduction invalid? Explain the basis for the rule that applies.
1. U v H
2. U / .. ~H