Hi vivek,
This can be done in XAML itself using Triggers.
XAML :
Include the below in Grid.Resources or in Window
<Style x:Key="ch" TargetType="CheckBox">
<Style.Triggers>
<DataTrigger Binding="{Binding ElementName=check2, Path=IsChecked}" Value="False">
<Setter Property="IsChecked" Value="True"/>
</DataTrigger>
</Style.Triggers>
</Style>
And assign this style to a checkbox, lets say CheckBox1 by doing in this way :
<checkbox name="check1" style="{StaticResource ch}" />
What this trigger does is that, it will check the value of Checkbox2's IsChecked property. If its false, then check1's IsChecked value will be true(like you wanted it to be inversed).
If you don't want the values to be inversed then, it can be down straight away in check1 by doing this :
<checkbox name="check1" ischecked="{Binding ElementName=check2, Path=IsChecked}" />
Hope it helped!