The indeterminate state can be used when there is a parent checkbox and 2 or more child checkbox's associated with the parent checkbox.
When all the child checkboxes are checked, the state of the parent checkbox is checked. When none of the child checkbox's are checked then the state of parent checkbox is unchecked.
The state of the parent checkbox is indeterminate when few of its child checkbox's are checked and few are unchecked.
The indeterminate state can be set using JavaScript, not with HTML.
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