THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS TRUE.
&
Q:

THE SENTENCE ON THE OTHER SIDE OF THIS CARD IS FALSE.

now let us assume P is true which means Q is true.Now Q says P is false ,a contradiction,so P is false.

From above we concluded P is false so it means Q is false(what P says of Q is wrong).Now Q being false says wrong about P.Thus, P is true ,again contradiction.

This way we can start with Q and show that it too has no truth value(neither true nor false).

So, these statements mean nonsense although individually they seem to be logical statements.