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I have two checkbox columns E and F. I want F to be the "superset" checkbox column, meaning that every checked cell in E means the corresponding cell in F must be checked as well.

I can populate column F with something like = IF( E3 = TRUE, TRUE, FALSE); however, this way the unchecked boxes (corresponding E cells are FALSE) won't get triggered by mouse clicks. How can I achieve this?

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In order to mark as checked a checkbox when other checkbox is checked but still able to uncheck/check the first checkbox directly you will have to use an on edit / on change Google Apps Script trigger.

For a general overview about extending Google Sheets through Google Apps Script, please read https://developers.google.com/apps-script/guides/sheets

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