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Gmail: how to filter messages from a specific sender into inbox if they have either of two keywords, and delete all messages with neither keyword

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I'm working for a nonprofit that serves people charged with federal crimes. We track their cases online using a system that sends an email to us every time something happens in their case. That's a huge amount of email though, and up to this point we've only really cared about sentencing hearings. So I currently have it set up with the following filters:

Matches: from:(case-updates@app.com) sentencingDo this: Apply label "Sentencing Update", Never send it to Spam, Categorize as Primary
Matches: from:(case-updates@app.com) -sentencingDo this: Delete it

We've decided we also want to get emails that contain the phrase "Trial held." I'm pretty comfortable creating the filter that would get something with that phrase into my inbox and labeled, but I'm less clear on how to update the deletion filter. It seems to me there are two options for NOT/- filters with multiple queries:

  1. delete everything that contains both queries
  2. delete everything that contains either query
  3. delete everything that contains neither query

I want option number three. What should the filter look like? I could see 1 or 3 being what happens when you use an AND operator and 2 and 3 happening when using an OR operator...


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