Refresh some basic logical propositions (or statements):

implication: if P then Q (P

—>Q)inverse: if not P then not Q (-P

—>-Q)converse: if Q then P (Q

—>P)contrapositive: if not Q then not P (-Q

—>-P)contradition: if P then not Q (P

—>-Q)

Mathematically or logically speaking, if the implication statement holds, then the contrapositive holds, but the inverse does not hold, i.e., *if P then Q*, then we can get *if not Q then not P*, but we can not get *if not P then not Q*.

That’s all logics needed here and Let’s turn to the ambiguous English in daily life. James R. Munkres of MIT gave an example in _Topology_ (2nd edition, 2000, P.7):

Mr. Jones, if you get a grade below 70 on the final, you are going to flunk this course.

We adapt it in a logical implication form:

Mr. Jones, if P then Q, where

P: you get a grade below 70 on the final

Q: you are going to flunk this course

Considering the context, we can also get that the inverse holds: if you get a grade above er or equal to 70, then you are going to pass this course(if not P then not Q ).

Question: when do statistical programming, what types of logics you use?

Answer: Not all mathematically. *see*

if score<70 then grade="flunk"; ***_if P then Q_**;

else grade=“pass”; *;if not P then not Q