Facebook: How to hide ‘Work and Education’ from specific people

Make a friend list of those you do not want to see you online by clicking on Create New List.

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You can then move those individuals to the list by clicking on Add to List.

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Click on Chat in the lower left corner.

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Then toggle the offline status (green toggle next to the list name) of that particular friend list.

Although there is no control to hide this, it will only show a mutual friend to someone if one of the two people's friend lists are already visible. So if you hide your friend list, someone visiting your timeline will only see mutual friends that have their friend list visible to that person. So although Facebook makes it easier, the visitor can already tell that you and their other friend are friends by checking their other friend's friend list. If Facebook did not already display it, someone could just write a script to get the same information.