A check box can be a controlling field in a field dependency:
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A. B.A.
The answer is: A. True.
In Salesforce, a controlling field is a picklist field that controls the values available in another field. When you create a field dependency between two picklist fields, you can specify which values in the controlling field map to which values in the dependent field.
However, it's not limited to picklist fields only. A checkbox field can also be a controlling field in a field dependency. This means that if a checkbox field is selected or cleared, it can control the values available in another field.
For example, let's say you have a checkbox field called "Premium Customer" on the Account object, and a picklist field called "Support Level" that is dependent on the "Premium Customer" checkbox field. You could set up the field dependency so that when the "Premium Customer" checkbox is selected, the "Support Level" picklist field shows the options "Platinum" and "Gold". When the checkbox is cleared, the picklist field shows the options "Standard" and "Basic".
In summary, a checkbox field can be a controlling field in a field dependency, just like a picklist field can be. It all depends on how you want to control the available values in another field based on the selection or clearing of the checkbox field.