The question asks $\forall x \in \Bbb R$, if $x > 3$ then $x^2 > 16$. The solutions tell me to find all intervals/cases for $x$ and prove that for one of the intervals, the hypothesis $x > 3$ is true and the conclusion $x^2 > 16$ is false, and if that case pops up the statement is false, and otherwise true.
But can I just make my proof "let $x = 4$. Then this statement is false. QED."??
I'm just worried about losing marks on these types of questions, I'm told to prove something so that the person who is reading it can understand but I don't know when something is obvious or I need to explain it or not.