Logical thinking - solution

In the previous post I gave you a riddle, and now I'll tell you the solution.

The correct answer is: the card with "car" should be picked. Why? Because if on the other side of the car, there is NY, the statement will be false, otherwise it will be true (eg., car|Paris).

Why #2? When you pick up the card with "plane", on the other side there could be everything and it won't violate the statement (eg., plane|Houston). When you pick up the card with "Chicago" there could be also everything (eg., Chickago|bike), and it won't help us to precise our sentence.