R - subset multiple columns from checkbox group

I have a dataframe and a few checkboxes that relate to columns in the dataframe. The checkboxes default is all options being selected.

   **CHECKBOXES**
   Name checkbox -> "Liz", "Ben"
   City checkbox ->  "London", "Berlin", "NYC"

   **DATAFRAME**
   Name  City
    Liz  London
    Liz  London
    Ben  London
    Ben  London
    Liz  London

My problem now is when I deselect the London checkbox, the dataframe returned is empty which is the incorrect behaviour. I want to return a dataframe that corresponds to the checkboxes that are selected and if nothing is selected return an empty dataframe

My code

   if (!(is.null(input$Name)) & !(is.null(input$City))) {

      names <- input$Name
      city <- input$City

      my_df <- filter(my_df, (Name %in% names) & (City %in% city))

   }

   **CORRECT RETURNED DATAFRAME**
   Name  City
    Liz  London
    Liz  London
    Ben  London
    Ben  London
    Liz  London

"Liz", and "Ben" are still checked even if "London" is deselected.