The connection between rights and duties is that, generally speaking, if you have a right to do something, then someone else has a correlative duty to act in a certain way.

Question

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That is correct, rights and duties are often seen as two sides of the same coin. If someone has a right (such as the right to free speech), someone else (such as the government) has a duty to respect and protect that right. Similarly, if someone has a duty (such as the duty to provide healthcare to citizens), citizens may have a corresponding right to receive that healthcare.

The Connection Between Rights and Duties Is That, Generally Speaking