How to change a radio box from true to false using MVVM - mvvm

Question

So I have a radio button that I want to change from being unchecked to being checked based on if a button is clicked. So
the XAML code I have is:
<RadioButton GroupName="rdoExchange" Grid.Row="2" Grid.Column="0" x:Name="PauseRadioButton" Command="{Binding PauseCommand}" IsChecked="{Binding Path=check, Mode=TwoWay}" Margin="3"/>
And the View Model Code:
public string check = "True";
public void Reset(object obj)
{
check = "True";
}
private ICommand m_PauseCommand;
public ICommand PauseCommand
{
get
{
return m_PauseCommand;
}
set
{
m_PauseCommand = value;
}
}
private ICommand m_ResetCommand;
public ICommand ResetCommand
{
get
{
return m_ResetCommand;
}
set
{
m_ResetCommand = value;
}
}
private void SetProperty<T>(ref T field, T value, [CallerMemberName] string name = "")
{
if (!EqualityComparer<T>.Default.Equals(field, value))
{
field = value;
var handler = PropertyChanged;
if (handler != null)
{
handler(this, new PropertyChangedEventArgs(name));
}
}
}
}
I've left out the relaycommand code and several other parts that I feel would be irrelevant to solving the problem.

Answer 1

Would something like this work?
XAML:
<RadioButton GroupName="rdoExchange" IsChecked="{Binding Path=OptionOneChecked, Mode=TwoWay}"/>
<Button Command="{Binding ToggleOptionOne}" Height="20" />
View Model:
public class ViewModel: NotificationObject
{
private bool _optionOneChecked;
public bool OptionOneChecked
{
get { return _optionOneChecked; }
set
{
if (value.Equals(_optionOneChecked)) return;
_optionOneChecked = value;
RaisePropertyChanged("OptionOneChecked");
}
}
public ICommand ToggleOptionOne
{
get { return new DelegateCommand(() => OptionOneChecked = !OptionOneChecked); }
}
}
using the NotificationObject class from the PRISM NuGet package.