Richards change, is correct: think about what happens when you use "||" instead:
If the selected item is "Bishop" than it isn't "Pawn" - result == true.
If the selected item is "Pawn" than it isn't "Bishop" - result == true.
If the selected item neither "Bishop" nor "Pawn" - result == true.
With "&&" instead it works better:
If the selected item is "Bishop" - result == false.
If the selected item is "Pawn" - result == false.
If the selected item is neither "Bishop" nor "Pawn" - result == true.
But that won't help you with what you are trying to do, as the values remain in the combo box unless your code specifically removes them.
What you need to do is keep a "chess board" - a 8 x 8 array of pieces - in your memory. When he the user adds a piece, put it in the appropriate array location.
When he checks the "Test" button, scan through all the pieces on the board (by looking at the array) to find for what items are placed on it.