This is a question from my discrete math quiz.
I was asked to prove there exists a Q(x). I used Disjunctive Syllogism to prove it. I was marked incorrectly because I used two different variables in the syllogism. My view is the variables can be implicitly the same, and I don't think this is incorrect. What do you think?
I agree with the instructor: $Q(a)$ follows from $(4)$ and $(1)$, but $Q(c)$ does not follow from $(4)$ and $(2)$, because there is nothing to justify the assumption that $a=c$, which is required in order to derive $Q(c)$ from $(4)$ and $(2)$.