Question: 1 judge each of the given statements as true or...
1. Judge each of the given statements as true or false and explain your reasoning in full sentences. A mere word by word rendition ("there exist x such that for all y..") is not an explanation. If a statement is false, explain why it is false by forming the formal negation, and explaining why the negation is true. (2 pts each, one for the truth value, one of the explanation.)
a. ∃x ∀y (y > x).
b. ∀y ∃x (y > x).
c. ∀x ∀y (y > x).
d. ∃x ∃y (y > x).
e. ∀y ∃x (x + y = 2).
f. ∃x ( x = 0 → x = 1).
g. ∀y ∃x ( xy > 0 → xy < 0).
2. For each of the following arguments, identify the argument form used. Just give the name. You do not have to justify your answer. (2 pts each)
a. I’m a vegetarian. Vegetarians don’t eat meat. Therefore, I don’t eat meat.
b. Jane is a member of the fans of Star Wars or Star Trek club. She is not a fan of Star Wars. Therefore, she is a fan of Star Trek.
c. On weekdays, Karl works. On weekends, he plays computer games. Therefore, Karl always works or plays computer games.
d. Cat owners spend money on cat food. I don’t spend money on cat food. Therefore, I am not a cat owner.
e. If we increase our space budget, we can build a moon base. If we can build a moon base, we can build a Mars base. Therefore, if we increase our space budget, we can build a Mars base.
f. Alex smokes. She also has a pre-existing condition. Therefore, her health insurance categorizes her as a “smoker with a pre-existing condition”.