Question about Sufficient and Necessary Assumption Negations?

sushilover930

Hi everyone, I hope your long weekend is going as good as mine with all this studying going on (simply fantastic). -_-

Just a bit of background, I've completed the Powerscore Bibles and am now going through the 7Sage core curriculum. When going through Sufficient and Necessary conditions, I had a quick question: how would you "draw" these two sentences?

1) No dog is funny (https://7sage.com/lesson/basic-translation-group-4-flashcards/) - Group 4

2) There is no reward without hard work. (https://7sage.com/lesson/basic-translation-group-3-flashcards/) - Group 3

Based on the CC lesson, "No" is the identifier for the first sentence, meaning we take either of the ideas (dog or funny), negate it and make it a necessary condition.

Based on the CC lesson for the second sentence, "Without" is the identifier for the second sentence, meaning we take one of the ideas "no reward" or "hard work", negate it and make it a sufficient condition.

My question is, why is the idea in the second sentence "no reward" but the idea in the first sentence just "dog"? Why doesn't the "no" negate the dog as well, just like it negates the reward, making it "no reward"?

Sorry if I confused you guys. Thanks so much!

Lime Green Dot

So for the diagram, I believe it would be these:
1) D ---> ~F | F ---> ~D
2) R ---> HW | ~HW ---> ~R

I usually think of these more intuitively rather by the group designations... but if your understanding is that for # 2, "without" goes together with "hard work (HW)," then your logic of negating one part (let's say we negate HW, so it looks like this: ~HW) and making it the sufficient condition would render the other part (in this case, "no reward," so it looks like: ~R) the necessary condition. All this simplified is the second translation, or contrapositive, I wrote above: ~HW --> ~R

For # 1, you have it exactly right that it only applies to one part, either "dog" or "funny." So you can see that the difference in # 2 is the presence of "without" = another way of saying "no." So we could actually say # 2 another (grammatically incorrect) way for clarity: "There is (no reward) if there is (no hard work)."

So the double negative makes # 2 different from # 1. Does this make sense?

sushilover930

Thanks so much, yes it does!