Which one of the following could be the schedule of advertisements?
Yuzhuo-CaoApril 5, 2023
Rule 2 Question
Why/how is rule 2 illustrated as "sufficient necessary"? There is no "if" or other indicators. This is not explained in the explanation. Seems to be a good illustration, but why, how?
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Hi, great question! I think this goes to the core of what sufficient and necessary is. My favorite way to understand sufficient and necessary relationships is that of a guarantee. That is, the sufficient condition guarantees the necessary condition. The most common way to think about this is "if X then y " which we can easily see means "X guarantees Y."
This is true of all the other common sufficient and necessary indicators we see like all, none, unless, and only if.
However, it is possible to have a guarantee without one of those common indicators. For example, the phrase "The sky is blue" guarantees that if something is the sky, then it is blue, and if something is not blue, it cannot be the sky. The second rule falls into this category of a guarantee without traditional conditional language.
That said, I would not worry too much about having a sufficient and necessary relationship sneak up on you. Personally I would not have diagramed the second rule as sufficient and necessary, and would rather have said something like "2=4, not 3." Ultimately however, I do like the tool of thinking about sufficient and necessary as a guarantee.
