Monitoring your kid/s?

Would you monitor your childs internet/phone privileges? I'm talking to the extent of putting a lock on the router allowing them to only see age appropriate content. (Basically permanent safe search). As well as knowing their social media logins and having their activities on the phone logged and sent to your phone or laptop. With the ease and quickness false, harmful information the internet and phones can dish out, would you consder this?

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