recently I got this question on my Logic Design course exam,

Prove the following theorem using postulates:

X OR 1 = 1

I explained it using a simple argument,

a variable can be considered as a switch in a circuit, if it is 1 then the switch is on, if it is 0 then the switch is off. The OR operation acts like if we would have switches wired in pararell, since in the case of (X OR 1) one switch would be always on, thus the current would always flow which means that the output of X OR 1 would always be 1 no matter of X, thus we have shown that the statement is obviously correct.

Strangelly the person grading the exam wasn't very pleased with this explanation, guess it was to "obvious", I got 0 points whitch I don't like. Anyway, I am asking

are you allowed to prove theorems with postulates?, Since a postulate is NOT an axiom, that means that the postulate is not necessary something that is a perfect choice to do profs with, axiom is. I understand why would I want to prove things with axioms, but why would I want to prove things with postulates??? Doesn't make sense to me.

Just one more thing, I noticed that on the exam, the gradient symbol(upside down triangle) was used to denote XOR operation, is that allowed? Isn't gradient a reserved symbol and should not be reused for something other than gradient?