代写PHIL 211 Homework 1, 2024代做Prolog
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Due-date: Please submit on Nuku by Wednesday 20th March, 2024. (Handwrittenu answers photographed on your phone is fine.) Total of 30 points. provided (1 pt each)
A. Symbolize the following in Propositional Logic (PL), using the dictionary
Dictionary:
Roger is a rabbit: R
Caplin is a capybara: C
Capybaras are gregarious: G
Dave is a rabbit: D
There are zoos: Z
1. Roger is a rabbit and Caplin is a capybara.
2. If Roger is a rabbit then Caplin is a capybara.
3. Caplin is a capybara, if Roger is a rabbit.
4. Roger is a rabbit only if Caplin is a capybara.
5. Roger is a rabbit if and only if Caplin is a capybara.
6. Caplin is not a capybara unless capybaras are gregarious.
7. Unless Caplin is not a capybara, Roger is a rabbit.
8. It is not the case that Dave and Roger are both rabbits.
9. Either Dave or Roger is a rabbit and not both.
10. It is not the case that if Dave is a rabbit then there are no zoos.
11. If Dave is not a rabbit then Dave and Roger are not both rabbits.
12. If there are no zoos then neither Dave nor Roger is a rabbit.
13. Only if Dave and Roger are both rabbits, are capybaras gregarious.
B. Construct an example of each of the following (1 point each)
1. A valid argument with one false premise and a true conclusion.
2. A valid argument with one false premise and a false conclusion.
3. An invalid argument with a tautology as one of the premises.
(Here is an example to demonstrate:
Construct an example of a valid argument with a true premise and a true conclusion:
Premise 1: Wellington is in New Zealand.
Premise 2: Dunedin is in NZ.
Conclusion: Therefore, both Wellington and Dunedin are in NZ.)
C. Tautologies, contradictions and contingencies by truth table (2 pts each)
Draw a truth table for the following formulas and use this to determine whether each of them is a tautology, contradiction or a contingency. (No points without truth table).
1. ~(P & ~Q) VP
2. (P & P) P (Draw a 2 row truth table for this: a row for P=0 and a row for P=1)
3. (P Q) (Q P)
4. ((P & Q) R) (~R ~P) (Draw an 8 row truth table for this)
D. Validity by truth table (3 pts each)
Draw a truth table for the following arguments and use this to assess them for validity. (No points without truth table).