1. Use mathematical induction to prove or disprove in detail using the basis step and inductive step that “sum of the first (n-1) positive integers numbers is (n(n+1)) / 2”. What is the disadvantage of using mathematical induction here? Justify your answer.

2. Describe the Pigeonhole principle in a scenario when you need to visit three places but when you have time for only two places. If we consider the scenario in terms of function, what type of function will it be? Explain in your own words.[Consider the places as the domain set and time as the codomain set]