The correct answer is: Both A and B.
A modem is a device that converts digital signals from a computer into analog signals that can be transmitted over telephone lines. A router is a device that connects multiple devices to a single network, such as the internet. In order to establish an internet connection on a computer, both a modem and a router are required.
A modem is typically provided by an internet service provider (ISP). The ISP connects the modem to its network, which in turn connects to the internet. The modem then converts the digital signals from the computer into analog signals that can be transmitted over telephone lines.
The router is typically purchased separately from the ISP. The router connects to the modem and to the computer. The router then distributes the internet connection to all of the devices that are connected to it.
In some cases, a single device may combine the functions of a modem and a router. These devices are often called “gateways.”