We can use GroupName property for mutually exclusive RadioButton but what can we do if we want to use mutually exclusive ToggleButton? ToggleButton doesn't have like ability. Please, do look in RadioButton what can you see? Exactly, RadioButton is inherit from ToggleButton so we can set in Template property ControlTemplate of ToggleButton. So our RadioButtons will be look like ToggleButtons besides will have GroupName property.
