An oath (from Anglo-Saxon āð, also called plight) is either a promise or a statement of fact calling upon something or someone that the oath maker considers sacred, usually a god, as a witness to the binding nature of the promise or the truth of the statement of fact. To swear is to take an oath.
If you swear on the Bible or other holy book, you are sworn. If you choose otherwise, you are affirmed.
This is not a grey area. You must answer yes or no.
There is no 'other'