Wrong section. This section is for comments about the MacRumors website. (e.g. something doesn't work, you don't like the user interface, you have a bone to pick with policies, etc.)
To answer your question, show your mom your browser history.
As to apps, though (like Facebook app, as opposed to using Facebook website) probably most apps don't store a history that you can view, so no way to prove it. I guess you could show your timeline and chat history but I think if only reading, no way to prove it.
There is no central, unified place on iPhone to show usage history.
There is a highly technical log that the system and (most) apps write to, but it's not really for the purpose of tracking user activity. That but would require an expert to go through and interpret. Most of is stuff that goes on in background, and the log is VERY chatty, and most people wouldn't be able to make much sense of it.
[doublepost=1563565866][/doublepost]Oh. This is WEIRD. This actually just became a legitimate "Site Comments" post!
I see that you posted to
ForumsiPhone, iPad, and iPod TouchiPhoneiPhone
But... your post shows up in "Site Comments" section!