private void DG1_AutoGeneratingColumn(object sender, DataGridAutoGeneratingColumnEventArgs e)
{
    //Set properties on the columns during auto-generation
    switch (e.Column.Header.ToString())
    {
        case "LastName":
            e.Column.CanUserSort = false;
            e.Column.Visibility = Visibility.Visible;
            break;
        case "FirstName":
            e.Column.Visibility = Visibility.Visible;
            break;
        case "CompanyName":
            e.Column.Visibility = Visibility.Visible;
            break;
        case "EmailAddress":
            e.Column.Visibility = Visibility.Visible;
            break;
        default:
            e.Column.Visibility = Visibility.Collapsed;
            break;
    }
}

private void CheckBox_Checked(object sender, RoutedEventArgs e)
{
    //Make each column in the collection visible
    foreach (DataGridColumn col in DG1.Columns)
    {
        col.Visibility = Visibility.Visible;
    }
}

private void CheckBox_Unchecked(object sender, RoutedEventArgs e)
{
    //Get the columns collection
    ObservableCollection<DataGridColumn> columns = DG1.Columns;

    //set the visibility for each column so only 4 columns are visible
    foreach (DataGridColumn col in columns)
    {
        switch (col.Header.ToString())
        {
            case "LastName":
                col.Visibility = Visibility.Visible;
                break;
            case "FirstName":
                col.Visibility = Visibility.Visible;
                break;
            case "CompanyName":
                col.Visibility = Visibility.Visible;
                break;
            case "EmailAddress":
                col.Visibility = Visibility.Visible;
                break;
            default:
                col.Visibility = Visibility.Collapsed;
                break;
        }
    }
}