Something is wrong with me today. I need a correction to my correction: you->should.
I was trying to get at the difference between chosing an single item from a set (described in your post) versus evaluating the group of items from sets that satisfy the proposed conditions.
Perhaps, as CookingWithGas said, I am confusing set theory with boolean logic.
The problem is that Boolean logic is inadequate for formalizing natural language. If you want a reasonable expression of natural sentences in logic, you need a system with more capabilities. A natural language “and” that isn’t between two complete sentences just doesn’t correspond to anything in Boolean logic.
What do you mean by “logically equivalent”? Both are structurally ambiguous and both have one interpretation that is close to one of the other sentence.
“I ate lunch and got gas at Joe’s truck stop.” is the latest incarnation of an old joke, playing on the fact that “got gas” is ambiguous–it can mean “filled up the tank of my car” or “had flatulence”.
“I got gas and ate lunch at Joe’s truck stop.” is not ambiguous. It states flatly that I ate lunch and filled up the tank of my car at Joe’s truck stop.
With the first sense of “got gas”, the two are equivalent, and if anyone were to utter this sentence, that’s most likely what they’d mean.
Not necessarily. Conversational “or” can be exclusive or not, depending on the context. In the cookie or candy bar example, exclusivity is implied. But what about “You can go to the dance if you’re a member of the club or the date of a member.”? It’s probably safe to conclude there that if two members are dating each other, they can both go to the dance. So someone can go to the dance who is a member and the date of member, so in this context, conversational “or” is inclusive.
Oh, boy. Just don’t anyone bring up the mapping of conversational “if/then” to logical P->Q.
Ooops. I just did.
:: runs away ::
Yeah, I was going to say this too. “Would you like some coffee, or a piece of cake?” doesn’t mean that the host is stingily permitting only one item to their guests. This would be Boolean OR; “and” wouldn’t work because it implies that the guest is obliged to accept both or (that is, XOR) neither.
Some languages do have different words for OR and XOR, but I’ve yet to run into one that really uses them according to Boolean logic. And they tend to become stranger when negated.
They can also be read that you ate lunch (somewhere, not necessarily Joe’s) and got gas at Joe’s truck stop.
I think Bashere has answered your main question correctly. If you want a Cat and a Black but not necessarily a Black Cat then you ask for them seperately.