Better wording would be appreciated on the following question.
True or false, an expensive knife can be made sharper than a cheap knife?
This is true. An expensive knife CAN be made sharper than a cheap knife. Also, a cheap knife CAN be made sharper than an expensive knife. You need to highlight that this is about the limit of potential sharpness. Maybe rewrite as:
True or false, an expensive knife can be made sharper than a cheap knife can?