Do we include the internal resistance of cell while calculating equivalent resistance of network? Take, for instance, the question given. Do we include the 1 ohm internal resistance while calculating equivalent resistance of the network?
From the wording "A network [...] to a battery with internal resistance" I would say the network is everything except the battery, where the battery consists of the ideal voltage source and the $1\,\Omega$ resistor. It is impossible to know for sure though what the author really meant.