Undergrad Weird statement of conditions in propositional logic

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In propositional logic, various phrases express the conditional "if p, then q," including "p is sufficient for q" and "q is necessary for p." Understanding these statements can be challenging, as some seem counter-intuitive. Instead of memorizing, grasping the underlying truth table for p implies q can aid comprehension. Recognizing that some phrases are equivalent or converse can also clarify their meanings. A solid understanding of these concepts enhances logical reasoning skills.
Mr Davis 97
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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...
 
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Mr Davis 97 said:
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...
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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