Answer:
No, the government is not responsible for providing the internet to all citizens.
Explanation:
The main duty of any government is to protect its citizens. This is done by creating and carrying out laws, keeping goods relationships with other nations and by applying military force when necessary. Then the government should provide for its citizens, giving them access to education, health care and a functioning labor market. Then the government should invest in its people with interesting cultural, social or business opportunities.
Providing all citizens with access to the internet is a desirable trait of any government, it is, however, no a governments's duty. The government can ensure measures to promote incentive programs for using the internet but it can not guarantee its citizen the access to it.
