Which of these are tautologies in First-Order Logic?

Question

1. $Fx\lor\neg Fx$

2. $Fa\supset Fa$

3. $(a=a)\land\neg(a=b)$

My guess is that only #2 is a tautology. #1 is not a tautology because there can be multiple variable assignments?

Answer 1

Assuming F is a predicate, it must either be true or false for any variable assignment. Therefore, #1 is also a tautology in classical logic (called the law of excluded middle).