1.Consider the following statement, where the variables are of type "natural":

forall x: (x > 5) --> exists y: (y + 3) = z + x

Which of the following statements isfalse?

Select one:

a. The variables x and y are bound.b. The statement is true for any natural z.c. The statement is a proposition.d. Every variable in the statement is either free or bound.

2.How manyof the following statements are equivalent to the following statement:

"Every dog has a dog of its breed that is smaller than Cardie."

1) Every breed has a dog smaller than Cardie.

2) There does not exist a dog such that every dog of that dog's breed is not smaller than Cardie.

3) Every dog that is smaller than Cardie has the same breed.

4) There exists a dog smaller than Cardie that is the same breed as every dog.

3. let = {a, b} and let X be the language {a, bb}.

How many strings of length exactly 5 are in the language X*?