Mathematical Reasoning

1

The following statement (p → q) → [(~p→q)→q] is:

  1. a tautology
  2. equivalent to ~p → q
  3. equivalent to p → ~q
  4. a fallacy
2

The negation of the statement "If I become a teacher, then I will open a school" is

  1. I will not become a teacher or I will open a school
  2. Either I will not become a teacher or I will not open a school
  3. Neither I will become a teacher nor I will open a school
  4. I will become a teacher and I will not open a school