Step 1: Understand the two statements.
Statement I says the part of the antibody that binds the antigen is the paratope. Statement II says the part of the antigen that binds the antibody is the epitope. We must judge both.
Step 2: Picture how they fit.
An antibody and an antigen fit like a lock and key. Each one has a small special spot that touches the other.
Step 3: Name the antibody spot.
The exact spot on the antibody that grips the antigen is called the paratope. So Statement I is true.
Step 4: Name the antigen spot.
The exact spot on the antigen that the antibody grips is called the epitope, also called the antigenic determinant. So Statement II is true.
Step 5: Use a memory trick.
Paratope is the part of the antibody, and epitope is on the antigen. Both spots must match for binding to happen.
Step 6: Decide the option.
Since both statements are correct, the right choice is that both are true.
\[ \boxed{\text{Both statements I and II are true}} \]