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Print True or False in calculated column using ARRAYFORMULA

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I need to output either TRUE or FALSE in column E, based on the following criteria:

If A2 = "stackexchange" then (always, regardless of other data) print TRUE in E2 (otherwise print FALSE)

If B2=FALSE AND C2=FALSE AND D2=False then print TRUE in E2 (otherwise print FALSE)

Example data and expected result

ABCDE
stackexchangeTRUEFALSEFALSETRUE
redditFALSEFALSEFALSETRUE
redditTRUEFALSEFALSEFALSE

The other requirement is that it needs to use ARRAYFORMULA as this data comes in automatically so the formula needs to be automatically copied to the rows beneath as they come in.


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