Let P(x) = x is blue. Let Q(x) = x is a kangaroo. Let R(x) = x can leap tall buildings in a single bound. Let S(x) = x wears a cape.

Suppose that the domain consists of all animals.

a. Express each of the following statements using quantifies, logical connectives, and the functions defined above.

i. No kangaroos are blue.

ii. Some kangaroos wear capes.

iii. All animals that wear capes can leap tall buildings in a single bound.

iv. Blue kangaroos do not wear capes.

b. Determine if the following arguments are valid and explain why or why not.

i. If ii. and iii. from part (a) are true, then some kangaroos can leap tall buildings in a single bound.

ii. If i., iii. and iv. from part (a) are true, then blue kangaroos cannot leap tall buildings in a single bound.