I thought through an example that shows how/why 2+ necessary conditions joined via conjunction are independently necessary, as the lesson states. Maybe it'll help:

Example statement: "I am happy only if my team wins and I score."

In lawgic: H → TW + IS, as "only if" is a Group 2, necessary condition indicator

The contrapositives would be:

/TW → /H, or more elaborately, /TW + IS → /H (Even if I do score, as long as the team loses, I am not happy)

/IS → /H, or more elaborately, TW + /IS → /H (Even if the team wins, if I do not score, I am not happy [selfish, lol!])

And together these both also imply, /TW + /IS → /H (If the team loses and I do not score, I'm definitely not happy)

So we can say the two necessary conditions are "independently necessary" overall, because as long as one fails in the contrapositive, then the sufficient condition also fails.

Is this...right??

#feedback

Someone pointed this out in an older comment, but "the only" is actually a Group 1 indicator!

Took me 20 minutes to figure this out, thanks so much for this comment!!!