You got exclusive ORs (XOR) and inclusive ORs (OR). A XOR B is true for A true or B true, but not for A and B true. A OR B is true for A true, B true or A and B true. I.e., A and B with the same truth value gives a false XOR but a true OR value. If neither A nor B is true then A XOR B and A OR B are both false.