public class MainWindowViewModel : INotifyPropertyChanged
{

    private bool _isVisible;
    public bool isVisible
    {
        get { return _isVisible; }
        set
        {
            _isVisible = value;
            NotifyOfPropertyChange("isVisible");
        }
    }

    public MainWindowViewModel()
    {

        Window1 X = new Window1();
        isVisible = false;
        X.Show();
    }

    public event PropertyChangedEventHandler PropertyChanged;
    protected void NotifyOfPropertyChange(string name)
    {

    PropertyChangedEventHandler handler = PropertyChanged;
        if (handler != null)
        {
            handler(this, new PropertyChangedEventArgs(name));
        }
    }
}

<Window.Resources>
        <BooleanToVisibilityConverter x:Key="BooleanToVisibilityConverter"></BooleanToVisibilityConverter>
    </Window.Resources>
    <Window.Visibility>
        <Binding Path="isVisible" Converter="{StaticResource BooleanToVisibilityConverter}" />
    </Window.Visibility>