I don't understand the last paragraph "The only problem is that you made up your own premise B -> A. The actual premise is A -> B. You confused sufficiency for necessity."

The rest of the lesson makes sense, but I'm totally lost when I read that. Maybe make a video or remove/clarify that paragraph? I don't see what that really adds here.

to prove that "not just for its value as an investment" isn't necessary it can be rewritten as "/investment AND investment".

So when you take the contrapositive you get "investment OR /investment", which satisfies every possible condition.

@kyorofan20 this clicked for me, so thank you.

it helped me to remember "if" and "only if" determine the sufficient and necessary conditions. Please someone correct me if I'm wrong here.

Example 1a: valid conclusion

1. A movie can be rated R only if the content is deemed too scary for children under 17.

2. The movie "Saw" is rated R.

3. Therefore, "Saw" has content that is deemed too scary for children under 17.

R -> too scary

Saw^R

---------

Saw^too scary

Valid logic form

Example 1b: invalid conclusion

1. A movie can be rated R only if the content is deemed too scary for children under 17.

2. "Saw" has content that is deemed too scary for children under 17.

3. Therefore, the movie "Saw" is rated R.

R -> too scary

Saw^too scary

---------

Saw^R

Invalid logic form

Likewise, changing the indicator to "if" swaps these examples.

Example 2a: Invalid conclusion

1. A movie can be rated R if the content is deemed too scary for children under 17.

2. The movie "Saw" is rated R.

3. Therefore, "Saw" has content that is deemed too scary for children under 17.

too scary -> R

Saw^too scary

---------

Saw^R

Invalid logic form

Example 2b: Valid conclusion

1. A movie can be rated R if the content is deemed too scary for children under 17.

2. "Saw" has content that is deemed too scary for children under 17.

3. Therefore, the movie "Saw" is rated R.

too scary -> Rated R

Saw^too scary

---------

Saw^R

Valid logic form