What is the difference between the words required and sufficient? How is it different to say $100 is sufficient to have a good time vs saying $100 is necessary to have a good time?
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This is a very important question, because you will be tested on this principle frequently. I will give you an introduction, but you should also watch the sufficient and necessary lesson and practice with drills.
I'll use your examples.
"$100 is sufficient to have a good time." Basically, this means that $100 will guarantee a good time. If I have $100, I will have a good time, no exceptions. We would diagram it like this: sufficient ---> necessary $100 ---> GT However, note that I can still have a good time even if I am broke. $100 dollars will guarantee that I have a good time, but it is not the only way to do so.
"$100 is necessary to have a good time." Contrary to the first example, $100 does not guarantee a good time. However, $100 is required. If I do not have $100, then I will not have a good time. The diagram looks like this: GT ---> $100 conrapositive: not $100 ---> not GT
SOULCAGES71on October 14, 2020
So just to be clear, is it a matter of how the statement is phrased?
Example 1:
If I choose to say that, "If I have a $100, I WILL have a good time." where "If" introduces a sufficient condition "$100" and the necessary condition would be "good time"
$100 --> GT contrapositive: not GT --> not $100 or, if I do not have a good time, it's because I did not have a $100.
Example 2:
What if I choose to say, "If I have a good time, it's because I have a $100 in my pocket." where "If" introduces the sufficient condition "good time" and the necessary condition would be "$100"
GT --> $100 contrapositive: not $100 --> not GT or, if I do not have a $100, I did not have a good time.
