I want to know if is safe download programs by software center and ubuntu software.
Thank you very much.
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Ubuntu software (and the former software centre) generally uses apt for it packages and serve merely as a graphical interface for the same thing you can do with apt-get. Any package in the system can potentially have regressions (bugs that can cause issues) or security issues, though these are often fixed over time. It's for those two reasons why you recieve updates, and even more important why you should always run a supported version of Ubuntu and keep it up to date (if security and stability is of priority for you). Don't let this worry you though, this is the same with just about every OS out there and certainly isn't limited to Linux based OSes like Ubuntu.
In addition, sometimes when you're browsing the web you might be tempted to setup a PPA or to add a repository. Whenever you're adding repos that are not supported or maintained by Ubuntu you do run the risk of pulling down packages that aren't considered "safe", as the latest version of a particular package will always be pulled down from any repo unless otherwise pinned or the package is held. These packages could be unmaintained and have security vulnerabilities, or have regressions that could break the system.
Of course, if you're just using vanilla Ubuntu and not doing the above, then you'll be as safe as anybody else running Ubuntu, so have fun and feel free to use Ubuntu Software/Ubuntu Software Centre as often as you want.