The correct answer is C. Share information and/or share peripheral equipment.
A LAN (Local Area Network) is a group of computers and other devices that are connected together so that they can share information and resources. Computers connected to a LAN can share files, printers, and other devices. They can also communicate with each other and access the internet.
Option A is incorrect because computers connected to a LAN do not necessarily run faster. In fact, they may run slower if they are all trying to access the same resources at the same time.
Option B is incorrect because computers connected to a LAN do not necessarily go online. They can only access the internet if they are connected to a router that is connected to the internet.
Option D is incorrect because computers connected to a LAN do not necessarily use e-mail. They can use e-mail if they are connected to a server that provides e-mail services.
Option E is incorrect because computers connected to a LAN can do all of the things listed in the other options.