I am Confused, mixing predicates and propositional letters?

Question

In the exercises at the end of each section the author gives you the Arguments and ask you to determine the validity of it, he then goes on and gives you the proper predicates to use which are located in the parentheses

If Round Robin won the race, then some people who were at the track were happy. If everyone who bet on the race lost money, then none who were at the track were happy. Therefore, if Round Robin won the race, then someone who bet on the race did not lose money. (R, Tx, Hx, Bx, Lx)

If the team wins, then someone in the backfield is a good tailback. Adams is a good tailback. Therefore, if Adams is in the backfield, the team wins. (W, Bx, Tx, a)

However some of the Arguments (very few of them in fact) like the examples I gave above contain capital letters 'R', 'W'

Im confused what exactly are these? Are these just simply propositional letters such as 'P, Q, etc'. So for example the first sentence in the first example would be symbolized as:

R $\implies \exists x(Tx \land Hx)$

and the first sentence in the second example would be:

W $\implies \exists x(Bx \land Tx)$

But then strictly speaking these above are not formulas and if the argument is invalid I have no way of giving an interpretation proving its invalidity.

Answer 1

Yes you are correct, up till this sentence:

But then strictly speaking these above are not formulas

$$R \implies \exists x(Tx \land Hx)\\ W \implies \exists x(Bx \land Tx)$$

These are in fact sentences, i.e., closed formulae. They contain no free variable.

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Addendum

so if I want to give a interpretation of these capital letters W and R, I simply treat them as propositional letters and for example could interpret W as “1 is a odd integer” or “the moon is made of green cheese”?

Yes, exactly. Or just 1=1 or 1≠1.