这是一个加拿大的数理逻辑限时测试代写，以下是具体作业内容：
For questions 1-4, symbolize the English sentence using the abbreviation scheme provided
for each question.
1. Athletes, who are fit, that don’t do a warmup get injured unless they are lucky. (4)
B: {1} is an athlete. D: {1} does a warmup. F: {1} is fit. K:{1} gets injured.
M: {1} is lucky.
2. Not everyone has a negative attitude despite the fact that no one is always happy.(4)
A: {1} is a person. B: {1} has a negative attitude. D: {1} is always happy.
3. A cat being cute is sufficient for them to be pet by someone, only on the condition
that they aren’t evil. (4)
A: {1} is a cat. C: {1} is cute. D: {1} is pet by someone. E: {1} is evil.
4. Among minds and ideas, either they exist or no one understands Berkeley. (4)
A: {1} is a person. B: {1} understands Berkeley. D: {1} is a mind.
F: {1} is an idea. E: {1} exists.
5. Translate the following symbolic sentence into an IDIOMATIC English sentence
using the abbreviation scheme provided. (4)
(Aa∧Ab∧Ac)∧((Ba∧Bb∧~Bc)∨(Ba∧~Bb∧Bc)∨(~Ba∧Bb∧Bc))
A: {1} is amazing. B: {1} is alive. a: Sharon. b: Lois. c: Bram.
6. Show the following argument is valid using a derivation. Use only the basic rules:
MP, MT, ADD, MTP, ADJ, S, R, DN, CB, BC, EI, EG, and UI. (10)
∃w(Bw∧Fw)→∃w~Hw. ∴ ∀x(Fx→~∀z(Bz∧Hz))
7. Show the following argument is valid using a derivation. You may use the basic rules
as well as the DERIVED RULES: CDJ, DM, NC, NB, SC, and QN. (8)
~∃z(~Hz∧~Bz). ∴ ~∀x∃y~(Hx∨By)
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