It is clear that none of the volleyball players at yesterday's office beach party came to work today since everyone w...

Shirnel March 4, 2020

No, Not Both, No One

Can you please clearly explain this to me. I didn't understand this in the learning video and don't understand why Mehran negated the first premise i.e. P==>AB

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SamA March 4, 2020

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

Shirnel March 6, 2020

Thanks for this Sam

Shirnel March 6, 2020

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?

Shirnel March 6, 2020

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

BenMingov March 20, 2020

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