Low Luck vs Random AA Casualties

[Unternehmer]

May the TripleA game have simultaneously the following rules?:

• random AA casualties

(property name='Low Luck for AntiAircraft' value='false'
property name='Choose AA Casualties' value='false'
property name='Random AA Casualties' value='true')

• low luck for air battles and normal battles

(property name='Low Luck' value='true');

So 'Low Luck for AntiAircraft' and 'Random AA Casualties' are mutually exclusive,
'Choose AA Casualties' and 'Random AA Casualties' are also mutually exclusive,

but are 'Low Luck' (for normal and air battles) and 'Random AA Casualties' also mutually exclusive?