No/None/Never + Unless/Without...

[lunalondon]

Hello PS,

I am struggling with the combination of no/never/none and unless/without/except/until.

From what I have understood with unless & co., we write whatever comes after unless on the necessary side and whatever comes before it on the sufficient side negated, as such:

A unless B = NOT A --> B
(Contrapositive: NOT B --> A)

And with never/no/none, we don't move things around and only negate the necessary side, but not the sufficient side, as such:

No As are Bs = (A --> NOT B)
(Contrapositive: B --> NOT A)

Say we now make the following combination:
A never happens unless B does - does this mean we apply both rules?

So: NOT A --> NOT B = B --> A?

Sorry about the long post, wanted to make sure I was being coherent! Thank you

[Kristina Moen]

Hi Luna,

No As are B means that the groups are mutually exclusive. You can use a double-not arrow for that one! A B

It means the same as you wrote:
A Not B
B Not A

But let's take another look at this sentence:
A never happens unless B does.

This means that B is necessary for A to happen. Which means you would just use the "Unless" Rule. Negate the sufficient side ("A never happens") and the part that comes after "unless" is the necessary. So this becomes A B. This means that if A does happen, then B must happen too.

Let's try another sentence:
There is no school today unless it stops snowing.
You would diagram that as: School Stops snowing.

Hope this helps!

[lunalondon]

Thank you!!