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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;
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