Weird statement of conditions in propositional logic

  • #1
1,462
44
So I am studying conditionals in proposition logic, and I have discovered that there are a variety of ways to phrase a conditional "if p, then q" in English. Some of the harder ones are...

p is sufficient for q
a necessary condition for p is q
q unless ~p (where ~ is the not operator)
p only if q
a sufficient condition for q is p
q is necessary for p

Do I just need to brute force memorize these? Or is there a way to really understand them? Some of them just seem so counter-intuitive...
 

Answers and Replies

  • #2
35,008
6,758
So I am studying conditionals in proposition logic, and I have discovered that there are a variety of ways to phrase a conditional "if p, then q" in English. Some of the harder ones are...

p is sufficient for q
a necessary condition for p is q
q unless ~p (where ~ is the not operator)
p only if q
a sufficient condition for q is p
q is necessary for p

Do I just need to brute force memorize these? Or is there a way to really understand them? Some of them just seem so counter-intuitive...
The second and fifth say the same thing in slightly different words.
The fourth is the converse of p if q (which is the same as if q then p).

An alternative to rote memorization of these is to understand the truth table for ##p \Rightarrow q##.
Code:
p.|..q...|..p → q
_________________
T.|..T...|....T
T.|..F...|....F
F.|..T...|....T
F.|..F...|....T
Hope that helps...
 

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