2. Quantifiers [20 points]

(a) [16 points] The following are four premises followed by a conclusion.

i. No birds except ostriches are at least 9 feet tall.

ii. I have no birds less than 9 feet tall.

iii. There are no birds in this aviary that belong to anyone but me.

iv. Chickens and ostriches are different birds.

v. There are no chickens in the aviary.

Express these statements using quantifiers and the following predicates: P(x) = x is an ostrich; Q(x) = x is at least 9 feet tall; R(x) = x is in the aviary; S(x) = x belongs to me; and C(x) = x is a chicken.

(b) [4 points] Show that the conclusion (statement v.) is valid.