If I command you to do something, I thereby permit you to do it. But suppose I command you to do A or B or both. Then it seems that not only do I permit the disjunction, but I also permit each disjunct.
It is, I think, necessary that if I command you to do something, I also permit you to do it. Working out why exactly would be interesting.
But I do not think it is necessary that if I command you to do A or B or both, then I permit you to do A and I permit you to do B. Imagine a case where you are under all sorts of orders that I have no authority to override and which I do not know all of, but I know that you're not both prohibited from doing A and from doing B. I might then say: "Do A or B or both. Of course, stay within the scope of your other orders." If one of your other orders is never to do B, you can't say that my disjunctive command permitted you to do B. If this is right, then it's not part of the fundamental logic of commanding and permitting that by commanding a disjunction one permits the disjuncts.
Interesting question. Is it ever morally licit to issue the command to do A or B or both, when B is morally illicit? It is, I take it, always wrong to command or permit something wrong (I distinguish permission proper from waiving punishment). If commanding a disjunction always involves permitting the disjuncts, it follows that one may not licitly command a disjunction when one of the disjuncts in it is wrong. But if it is possible to command the disjunction without permitting each disjunct, then it may be licit to command a disjunction one disjunct of which is wrong, though not a disjunction both disjuncts of which are wrong. We can imagine a situation where very bad things will happen (to you and to your subordinates) if you refuse to issue an order you were commanded to issue, and the order is to do A or B or both, and B is morally wrong. In that case, it may be licit to say: "I command you to do A or B or both. And I forbid you from doing B." You've fulfilled your order to the letter and haven't commanded or permitted anything wrong. Still, in ordinary contexts, commanding A or B or both carries the implicated (and still real) permission of doing A and of doing B and of doing both.
Suppose now I command you to do both A and B. Interestingly, while it does follow that I permit you to do both A and B, it does not follow that I permit you to do A. I may only be permitting you to do A if you're going to do B as well. So commands are not closed under logical entailment. For if they were, then in commanding A and B, I would be commanding A, and hence also permitting A.