Instructions: Complete each part of the assignment. Symbolization and proofs MUST be completed according to the rules and standards covered in class. Any other symbolization or proofs will not be graded. Complete the assignment on your own.
I strongly suggest that for your proofs you make use of tables in order to ensure as much clarity as possible. If a proof is unclear your grade will suffer if I can’t understand it!
Part 1 (6 pts). True or false? Explain your answers.
- It is possible for a valid argument to have false premises.
- If an argument has all true premises then it is sound.
- If an argument has a false conclusion then it cannot be valid.
Part 2 (14 pts). Translate the following claims into propositional logic. Provide a translation key.
- If it’s the case that you will go on vacation only if you get all your work done, then I guess we will never go.
- It is illegal to feed or harass the birds.
- “Unless philosophers become kings or kings philosophers, there can be no rest from troubles for states, nor yet for all mankind” – Plato
- It is necessary for university enrolment that you pay your tuition.
- I won’t go without my bag.
- You make take our lives, but you will never take our freedom!
- You can go to Waterloo or Toronto, but not both.
Part 3 (15 pts). Provide proofs for the following arguments.
- ~(AvB) ? ~(A&B)
- B?U, ~L?I, ? (~U&~I)?(L&~B)
- B?(T?G), T?B, ?G
Part 4 (9 pts). For each argument, identify each premise/conclusion as an A,E,I,O statement and identify the identify the major, minor, and middle terms. Are these arguments valid? Explain using the rules for evaluating categorical arguments.
- Some candidates in this election have been indicted.
- No one who has been indicted is a good candidate.
- Therefore, some candidates in this election are not good candidates.
- Some cloudy days are rainy days.
- Some rainy days are cold and windy.
- Therefore, some cloudy days are cold and windy.
- Every educated person can do logic.
- No educated person is unemployed.
- Therefore, no unemployed person can do logic.
Part 5 (16 pts). Provide a proof for this argument.
Sv(WvD), ? (SvW)vD