Conjunction vs Disjunction in Conditional Statements

serouj.sg

I have a question regarding Conjunction and Disjunction when they’re present in the sufficient and/or necessary condition.

I know “and” does not split in the sufficient condition and does split in the necessary condition and vice versa for "or" statements.

Does that mean if a statement says “A and B -> C” that we need both A and B to be present to trigger the necessary condition? Or 1 of them alone would be enough to trigger.

Conversely, if it said “A -> B and C”, does A being present mean both B and C must be present together as a consequence? Or one can be present without the other?

Thank you for taking the time to respond.

ntrepanier5

If I put on shoes AND socks, then I will go to the store.

I need both of those things to be met in order for the sufficient condition to be satisfied. If I forget my socks, I'm not going to the store. If I forget my shoes, I'm also not going to the store (especially bc I don't want to walk on the 100°F pavement!).

If the Uruguayan peso rises in value, then the economy will improve AND exports to Argentina will increase.

The Uruguayan peso rising in value is the sufficient condition, so it guarantees the occurrence of the necessary condition, which consists of the improving economy AND increased exports to Argentina.

Yeah, if A--> B AND C, then the occurrence of A guarantees the occurrence of all constituent parts of the necessary condition.