Sufficient or Necessary? Translating from English (Weird cases)

pokemon2020

Hello,

I was going over the concepts of necessary and sufficient conditions. Here are some terms I'm not sure how to interpret. Help would be appreciated:

"Assuming that A, B" or "B, assuming that A"

"As long as A, B" or "B as long as A" (also, "So long as")

"A provided that B"

"A on the condition that B"

Thanks!

ExcludedMiddle

I believe the first two would translate into conditional logic as A --> B. The last two are the reverse: B --> A. The phrases used should signal to you that there's a conditional relationship between A and B in each example. The phrases used are all introducing sufficient conditions - notice how in each case one guarantees the other. In the first two, you know that if you have A, you have B. In the latter two, you know that if you have B, A also obtains.

FixedDice

Let me take a stab at this...

The first and second phrases seem to be referring to the same idea, A -> B. They both designate A as a condition that allows B's occurrence. "As long as" and "so long as" mean the same thing, by the way.

The third and fourth phrases seem to be referring to a different idea, B -> A. They both designate B as a condition that leads to A's occurrence.

I'm not 100% sure though. Insight from the rest of y'all would be appreciated. This could be a learning moment...

ExcludedMiddle

I think it's tempting to see these as similar to the Group 2 logical indicators and get the wrong translation, but notice in the first two, for instance, that if you translate them as B -> A, it's basically the logical opposite of the phrases used, because they're telling you that A guarantees B, not that B guarantees A.