A student is asked to prove whether the following statement (*) is true or false:

(*) *For all real numbers $a$ and $b$, $|a+b|<|a|+|b|$*

The student's proof is as follows:

Statement (*) is false. A counterexample is $a=3,b=4$, as $|3+4|=7$ and $|3|+|4|=7$, but $7<7$ is false.

Which of the following best describes the student's proof?