Predicate Is Before The Subject Is This The Correct Translation?

Question

I'm trying to figure out what the proper translation in predicate logic would be for the example below, I'm confused because the predicate comes before the subject. So i'm wondering if I need to include it into the domain, or make it a separate domain predicate.

Example: "All orange basketballs are round."

I was thinking that I could translate this in one of two ways, which one of these would be correct?

"All orange basketballs are round."
Domain:
O(x) - x is Orange Basketballs
R(x) - x is Round

Answer 1- (∀x)(O(x)-->R(x)

OR

"All orange basketballs are round."
Domain:
B(x) - x is Basketball
O(x) - x is Orange
R(x) - x is Round

Answer 2- (∀x)(B(x)-->O(x)-->R(x))

I'm under the assumption that answer 1 seems more sound, but any advice is appreciated!

Answer 1

Just an adjustment on your (2), which is correct, if you parenthesize properly:

How about $$\forall x\Big((B(x)\land O(x))\to R(x)\Big)\tag{1}$$

which is equivalent to $$\forall x\Big(B(x)\to \big(O(x) \to R(x)\big)\Big)\tag{2}$$

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Below, you'll see the results when entering $(a \land b)\to c$, followed by the truth table resulting from $a \to (b\to c)$:

Answer 2

Each of those representations will work. Note, however, that you seem to neglect to specify the domain in each of the cases -- you write "Domain:" but nothing follows the colon.

In the first proposal, your domain would presumably be all basketballs.

In the second, your domain would could be everything in the world, or all sports paraphernalia.

Which of the possibilities you choose in a particular situation is not really a question of being correct, but depends on what is the most convenient and useful way to model the reasoning about balls, colors, and roundness you have in mind to use it for.

Of course, if you're just given the sentence as a homework exercise without any context, there's no actual reasoning to have in mind, so you can't use convenience and utility to make your choice (as you would in any real situation). Instead you'll have to guess at what the teacher would most like to see. If you're in a classroom situation where it is usual to specify a domain for the variables, choosing the first representation would give you a chance to show that in action.