When you first signed up for Facebook, you had the option to fill in a "relationship status" - this information is used on your public Facebook profile to let others know that you are "Single", "In a relationship", "Engaged", "Married", "In an open relationship", "Widowed", or "It's complicated"! Since things evolve, you will find yourself having to change or update your Facebook relationship status: this tutorial explains how to do this, how to show or hide your relationship status from other Facebook users (public, private, for friends only, etc.), and if you can do so without other people knowing (anyone, or Facebook users in particular).
To change the relationship status of your Facebook profile:
This is how easily you can change your relationship status of your Facebook profile! Note that when you supply the name of another Facebook member in your relationship, they will receive an email like this, and a notification and be able to confirm or ignore:
As mentioned above, you can set your relationship status to "blank" if you don't want to share this information; but Facebook also lets you set privacy levels for your relationship status, to let you hide it from some Facebook users but show it to others:
As you saw in the previous section, Facebook lets you customize the privacy and visibility of your relationship status: when you change relationship status, all these people will be able to see the new, updated relationship status if they go to your Facebook profile. Other than the person you optionally add as member in your relationship, other Facebook users won't receive a notice, even the former relationship partner.
In other words, Facebook offers you a convenient, "silent breakup" option. (Assuming no-one tells your boyfriend / girlfriend about the relationship status update, and that he or she does not notice the relationship change that automatically occurred on their profile as well, but the status will be changed silently.)
Depending on your partner's number of friends, their Facebook account settings and yours (you can make your recent updates invisible to some), they may come across your latest "Recent Activity" posts: