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Facebook allows each user to decide how much or little privacy they want. Before you post anything, you can decide who you want to see it: friends, certain groups of people, or a custom selection of people/groups. You can also block people who are harassing or bothering you, and then they cannot see or search for you.
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X Privacy Settings
X (formerly Twitter) makes it very easy to keep your profile private. If you protect your tweets, people cannot see them unless you accept a follower request from them. All requests have to be approved first, so you will know who is looking at your tweets. Be careful about accepting strangers because you never know who they may be.
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