# Question: 1 judge each of the given statements as true or...

###### Question details

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”.