Saturday, August 8, 2009

p->q <=> p only if q <=> q unless -p

Note: '-p' represents NOT p.

As an student whenever I learned above, I always used to be confused if the three were equivalent. Here is how I can remember them now.

Let say p = I'll eat banana.
q = Its not evening.

p only if q
The sentence, "I'll eat banana ONLY if Its not evening." is equivalent to "If I eat banana that means its not evening" which is p->q

q unless -p
The sentence, "Its not evening unless I'm not eating banana." is equivalent to "Its not evening if I'm eating banana" which is "If I'm eating banana then It's not evening" which p->q

One more important thing I learned is that mathematical logic statements have nothing to do with same in natural languages such as english, we draw this parallel just to remember them better. Natural language statements are often ambiguous but logic statements always have a precise meaning.

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