Why is the IsChecked property of a checkbox control in WPF of type bool? (or Nullable<bool>). I mean how can a checkbox control have the value of null?
Yes the null value exists and appears as a filled box. It indicates "Not Applicable" to the system.
According to the documentation, the IsChecked property has three different possible states:

So, when IsChecked is set to null, the check box will show an "indeterminate" state. This is commonly represented as a shaded, or greyed-out, control.
Checkboxes can have a 3rd, grayed, indeterminate state.
Don't forget to set the checkbox's property IsThreeState to true to enable this functionality.
Because WPF supports binding. If we bind a DB boolean column value to a checkbox. That column may have True/False/Null values. That means it has three values for a boolean field. So the WPF UI also should handle the three state.
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