No, Not Both, No One

Hello @Shirnel, "No one who was promoted during the past year failed to attend the awards banquet." This statement follows the format: No As are Bs. When creating a sufficient and necessary diagram, we negate the second term. If A, then not B. A - - - - - - - -> not B Let's apply it to this question. No promoted person failed to attend. If a person was promoted, that person did not fail to attend the banquet. P - - - - - > not FAB There is a double negative here, which I am guessing is what caused your confusion. Not failing to attend the banquet simply means attended the banquet. This is why we can say: P - - - - - -> AB Let's try one more example just to make this clear. No cats can swim. If it is a cat, then it cannot swim. C - - - - -> not S

Thanks for this Sam

So basically with no, not both, no one and none, the same rule applies. Pick one make a sufficient condition (anyone), negate the other and make the necessary condition. So for the following: No cats can swim. This could be: If it is a cat, then it cannot swim. C - - - - -> not S or it could be If you can swim, then you are not a cat S-----> not C I just simply need to pick one, it doesn't matter which one it is?

Actually scrap the above, I just realized that the second is the contrapositive.

@Shirnel, exactly! Please let us know if you have any other questions.