Identifying necessary and sufficient conditions in English (less clear cases)

Question

I understand how the material conditional works and it's really nice when using it in propositional logic, but in English I almost lose my mind trying to identify which part of a conditional sentence is necessary or sufficient.

Example:

"Jim can join our club, assuming that he's a good person"

"Parties subject to the aforementioned clause shall pay a fine no greater than $500.00 on the condition that they are over the age of 18"

"Provided that they all pay, the basketball team will be able to compete in the tournament"

Thanks!

Answer 1

Equivalent :

If A, then B.

B if A.

When A, then B.

B when A.

B provided that A.

A is (a) sufficient (condition) for B.

B is (a) necessary (condition) for A.