Show whether the following is true or false:
α |= β or β |= α, for any two formulas α and β
I'm assuming here that α and β are formulas, not a set of formulas. My thought is that I can prove that it is false if I show α doesn't entail β and β doesn't entail α. I tried using a truth table to help me with this problem, but it didn't seem to help. I'm not sure how to go about this problem. Any help will be appreciated.