I know it is illegal to post full articles of a website on yours beacuse of copyright.
Is it legal to post the rss feeds of a website on your website?
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It depends on the terms and conditions of the website whose work you are reproducing. The published works of others is copyrighted so you cannot reproduce it without their explicit permission which may be given in their terms of service. You should definitely contact them to ask them for permission before doing it.
FYI, Google is cracking down on copied content/scraped content so unless you have a good reason to reproduce the works of others, and you do it properly, I don't see much of a benefit to doing this. Anyone, the Internet doesn't need more copycats. Original work is much preferred.