Does Vodafone list what websites you have visited on the internet on the phone bill?

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Basically my question is, if my parents can see what websites I have visited on the internet when they receive the phone bill.
We are with Vodafone - 3MB Phone and Broadband package, if that helps.
Perhaps if anyone has that package or has Vodafone can tell me what it does tell you on your bill.
Thanks!

P.S. For any smart asses out there.........You know why I'm asking this question