[Ken Carman]

"Hobbes suggested that without government humans existed in a 'state of nature.'"

False. We are all part of "nature." "State of" is redundant, at best. Governments are made up of people, so governments are part of nature.

"This state of nature, consequently made humans brutish and evil."

And governments aren't?

"He thought that without a social authority humans had the right to take whatever from whomever."

Social authority often takes the stand it has a right to take whatever from whomever. Humans need to organize so as to protect themselves and improve their lot. That's how government starts. But evenb without some authority an authority eventually develops. In reality, humans need to both organize to protect and improve, and defend themselves from the very organizing efforts that screw up. Our forefathers had a good sense of this when in the Constitution they included that all rights not mentioned belong to the people.

"This way of thinking caused him to think that people in a state of nature should give up control to a strong central authority to provide rules for humans."

And this has been used by some of the most oppressive regimes in history to excuse their excesses. There's a false separation here between government and people. The assumption is that there will be some control to give up if there is no central authority. There will always be one, in reality, whether it's formulated by those attempting to create a society that's free, or grabbed by those whose interest is in gaining power for themselves at the expense of the governed. Some governments are more "centralized" than others. But centralization neither increases freedom, or necessarily destroys it. Depends upon who is in charge. Larger can mean more imposing, but smaller doesn't always mean less so.

"Hobbes constructed a set of nine laws within his book Leviathan giving humans natural rights and the ways they should act upon them."

Got link to these laws?

"Should humans sacrifice their 'natural rights' to preserve these rights?"

I find "natural rights" a meaningless phrase. We are either allowed the right, given the right, or it is taken from us. Then the assumption is you're giving up rights to preserve rights. Nonsense. Your giving up rights because someone wants power over you. Given certain examples, yes, the state should have power over us if we murder someone. No right should be absolute. But considering other "rights"... no way in hell.

(Also, I wonder about Hobbes. Did he get Calvin's approval first??? Chuckle.)