The third difference has to do with interrogative tags. These are sequences of a contracted auxiliary verb and a pronoun that you can put at the end of a sentence, such as isn’t it, doesn’t she, or am I, to turn it into a question. Usually, these come at the end of a declarative sentence, as in It’s hot, isn’t it?, but you can use the tags will you, won’t you, and would you after an ordinary imperative. For example, you could say Give me a hand, would you? or Keep it down, will you? This doesn’t work with first-person inclusive let-imperatives. Let’s go, will you? doesn’t make any more sense than You let’s go. On the other hand, you can say Let’s go, shall we?, which shouldn’t be possible at all if the subject of Let’s go is truly an understood you.
The fourth difference has to do with negation. If you want to suggest not doing something, there are at least two ways to do it with a first-person inclusive let-imperative. The most common way to negate Let’s go is Let’s not go, but another way is Don’t let’s go. They both mean the same thing. With an ordinary imperative, though, the way you negate it affects the meaning. For example, let’s consider an ordinary imperative sentence about a party. If your teenage kids say to you, Let us go to the party, it’s a probably a party that their friends are having, and they’re requesting permission to go. On the other hand, if they say Let us not go to the party, it’s probably a party your friends are having, and your kids are asking permission to stay home. And if they say Don’t let us go the party, it’s probably once again a party that their friends are having, but this time they don’t want to go, and they want you to give them a socially acceptable reason to avoid it: “Sorry, my boring, overprotective parents won’t let me.” That’s a pretty big difference in meaning.
The final difference for first-person let imperatives involves ellipsis—not the punctuation mark, but grammatical ellipsis. Ellipsis is the use of just a fragment of a sentence when the rest of it is clear from context. With an ordinary imperative, like Aaron’s Let us know when you arrive, someone else can second the request, and say, Yes, please do instead of saying the full sentence Yes, please do let us know when you arrive. Alternatively, they could negate the request by saying, No, please don’t. In contrast, with our Let’s go example, you can second the suggestion by saying Yes, let’s, or reject it by saying No, let’s not, but you can’t say, Yes, please do, or No, please don’t.