In my discrete math class I was given the following problem

Let A and B be sets of real numbers. Write the negation of

each of the following statements:

(a) For every a ∈ A, it is true that a^2 ∈ B.

(b) For at least one a∈ A,it is true that a^2 ∈ B.

Would the negation for each question be correct if I said:

For every a that is not an element of A it is not true that a^2 is not an element of B

and

For at least one a that is not an element of A it is not that that a^2 is not an element of B

ANy help provided would be appreciated. Also does anyone know any good books for discrete math to use as a reference? The class I am in does not have a required textbook we just work off your instructors notes.

Thanks

and