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.
