Breaking Apart Compound Statements

Can you please also address how the presence of quantifiers impacts the breakability of and/or statements, if at all?

Hi @JoshG, I've been wrestling with this question for about 2 hours now, reading every message and diagramming constantly. Thanks to some of the messages from @Sam and @Ravi, among others, I think (hope) I've finally got it. All of your statements are correct except for the first one. Carrots and Turnips are vegetables. C & T --> V I think that we would only use an "and" to combine sufficient statements when they are dependent on one another. Carrots and Turnips are independent variables, so they shouldn't be combined with "and." If we did diagram C & T --> V, it would mean that if an item were Both a Carrot And a Turnip, it must be a Vegetable. Or, as one of the instructors (Sam, I think) wrote, "All Carrots that are Turnips are Vegetables" I'm not sure, but maybe it should be diagrammed as C or T --> V "If it's a Carrot, or If it's a Turnip, it must be a Vegetable" If I've made any mistakes, please correct me. This is really hard for me, too.

Hi @JoshG and @Brett-Lindsay, Thanks for the question! Just wanted to confirm what @Brett-Lindsay said; all of those statements are correct except the first. Basically, we can break up “and” when it’s in the necessary condition, and we can break up “or” when it’s in the sufficient condition. When we have something that says A & B —> C That means that if something has BOTH properties A and B, then we can infer C. But if it just has one, then that might not be true, which is why we can’t break it up. For example, let’s say I will only go outside if the two conditions hold: it’s not raining, and a friend comes with me. Both of these conditions need to hold. So we diagram this Friend & ~Rain —> Go outside Now if we break this up, we would have Friend —> Go outside ~Rain —> Go outside But if we take those two conditionals separately, that means “friend” by itself would be sufficient for me going outside, whether or not it was raining. Or “not rain” would be sufficient for me going outside, whether or not I had a friend. But I want both conditions to be true before I go outside. So we can’t split up “and” in the sufficient like this. ?So it’s a bit tricky because when we say things like “carrots and turnips are vegetables,” we really mean “if something is a carrot, or something is a turnip, it’s a vegetable,” since both carrots and turnips are vegetables. So that would be diagrammed as C v T —> V The phrase C & T —> V Actually means that if something is both a turnip and a carrot, it’s a vegetable. It has to have both conditions be true. So something that was just a turnip wouldn’t be a vegetable, under this definition; it would also have to be a carrot. Hope this helps! Feel free to ask any other questions that you might have.

Thanks @shunhe. Great explanation! Understanding this stuff is taking a while, but it's coming.

"We can do this when there is an OR statement in the sufficient condition (as in the first sentence) or an AND statement in the necessary condition (as in the second)."