Which sentence in this excerpt from Common Sense by Thomas Paine supports the claim that the American colonies could thrive independently from Britain?
(1.) I have heard it asserted by some, that as America hath flourished under her former connection with Great Britain that the same connection is necessary towards her future happiness, and will always have the same effect. (1.) Nothing can be more fallacious than this kind of argument. (2.)We may as well assert that because a child has thrived upon milk that it is never to have meat, or that the first twenty years of our lives is to become a precedent for the next twenty.( 2.) (3.)But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her.(3) (4.)The commerce, by which she hath enriched herself, are the necessaries of life, and will always have a market while eating is the custom of Europe. (4.)

All the sentences support the claim that the American colonies could thrive independently from Britain. The one that does it more directly is number 3: But even this is admitting more than is true, for I answer roundly, that America would have flourished as much, and probably much more, had no European power had any thing to do with her.

Sentences 1 and 2 are simply explaining - by comparing the country to a child - how naive is the claim that, if America once needed Britain, it would always need Britain. It would be the same as saying a child will never eat meat because he/she was first raised my being fed milk.

Sentence 4 is only claiming America has found a lucrative livelihood by taking advantage of European habits and needs.

Sentence 3 makes it clear that, in Paine's opinion, America not only is successful but could have done even better if there had been no interference from Britain at all from the very start. Such connection was not essential for America's development, it only hindered it.