The following problem is taken from Exercise 1.7 in David Morin's "Special Relativity: For the Enthusiastic Beginner":
A train and a tunnel both have proper length L. The train moves toward the tunnel at speed $v$. A bomb is located at the front of the train. The bomb is designed to explode when the front of the train passes the far end of the tunnel. A deactivation sensor is located at the back of the train. When the back of the train passes the near end of the tunnel, the sensor sends a signal to the bomb, telling it to disarm itself. Does the bomb explode?
The solution given in the book is in the affirmative. It is certainly obvious from the train frame. Since the tunnel is length-contracted, the front of the train passes the far end before the back of the train passes near end of the tunnel. However, as seen from the tunnel frame, it seems we have a contradiction as the order of the two events reverses.
The resolution to this paradox given in the book says the deactivation device cannot instantaneously tell the bomb to disarm itself. A signal takes time to travel to the front of train, and it is calculated that, even if the signal has speed $c$, the transmission time is still longer than the time it takes for the front of the train to pass the far end of the tunnel. Thus, the bomb explodes in the train frame as well.
Nevertheless, the solution doesn't seem quite satisfactory to me. What if we change the question to "Does the deactivation sensor send a signal to disarm the bomb?" This certainly looks like a frame-independent statement and all observers must agree on whether or not the deactivation sensor initiate a signal.
Is the statement "The deactivation sensor sends a signal to disarm the bomb" frame-independent in the train-tunnel paradox? If yes, what is the correct answer to the above statement?
Edit: I don't think the proposed duplicate pinpoints the loophole behind the apparent "contradiction". The below two answers did a much better job clarifying my doubt.