Songs off iPhone 5 won't delete?

I swiped delete on my songs and I hit the delete button, but yet the songs are still there its just they have this cloud symbol next to it with a red arrow pointing down. I don't want them on my phone anymore to redownload, I want them DELETED. How do I solve this?

Subscribe to iTunes match so you can delete them permanently, otherwise go to settings, go to music then turn off show all music