Choose and define predicate symbols, and translate each of the following arguments into statements in predicate logic. then, taking all but the last statement of each argument as the hypotheses, and the last statement as the conclusion, assess the validity of the argument. if it is valid, give an informal proof that the conclusion is a logical consequence of the hy- potheses. if it is invalid, give an example of a possible domain that makes all the hypotheses true and the conclusion false. (a) (12 points) (the domain is the animals in a particular zoo. thus, in vx and 3x, the variable x refers to an animal in this zoo.) i. every animal that flies has wings. ii. every bird has feathers and wings. ii. no bird has six legs. iv. there is an animal that has six legs and flies. v. there is an animal that has wings but is not a bird. (b) (12 points) (the domain is some collection of birds, nests, and eggs. thus, in vx and 3.x, the variable x refers to a bird, a nest, or an egg in this domain.) i. there at least two nests. ii. all eggs are speckled or blue, but no egg is both. iii. some nest has both a speckled egg and a blue egg in it. iv. no bird will sit on a nest with fewer than two eggs in it. v. there is at least one nest that a bird will sit on.