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Too, also, and either are so tough for me.
Are the following sentences correct?
If they aren't, why is it?

You can't have your cake too.
You can't have your cake also.
You can't have your cake either.

I think the first sentence is incorrect because my textbook says it's incorrect but actually I don't understand why it's incorrect. Why is it incorrect?

I think the second sentence is correct and its meaning is the same as the third sentence. But I think if the second sentence is correct the first sentence should be correct because too means also. Why is the second sentence correct and the first sentence incorrect?

I think the third sentence is correct and its meaning is clear to me. But I don't understand why either, not too, should be used. Why should either be used instead of too?
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Comments  
The expression is
You can't have your cake and eat it too.

Too and also mean "in addition", so there has to be a something #1 and a something #2. Without 2 different "somethings" in sight, it is like a dangling "and"...
You would not say this:

I like cake and.

In the above sentence, something #1 is having your cake. Something #2 is eating your cake.

In some cases, the something #1 and something #2 are in separate sentences, but they are connected into one thought.

I want to go to college. My twin brother also wants to go to college, but our parents can not afford the expenses for both of us.

"I want some ice cream", my brother yelled.
"Me, too", I said. And then I added, "Please."

Here is either:

You can't have your cake, and you can't have your pie, either.
Thans for your nice reply!
I think I somehow got it, but am not sure (sorry!).

But "You can't have your cake and eat it too." is too difficult so I'd like to make my quetion simple, that is I'd like to think about the three sentences and the quesions in my first post. In other words, I'd like to understand the meaning of too, also, and either.

Would you teach me the questions in my first post?
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The following are all correct. Note that usage depends on the kinds of similarities and contrasts.

1. You can have your pie, and you can have your cake too. (same as the pie -- both can)

2. You can't have your pie, and you can't have your cake either. (same as the pie -- both can't)

3. You can have your pie, but you can't have your cake too. (opposite of the pie - can first)

4. You can't have your pie, but you can have your cake. (opposities - can't first)

5. You can have your pie, and you can also have your cake. (alternate way of saying 1.)

CJ
northwindYou can't have your cake too.
You can't have your cake also.
You can't have your cake either.
I will try another time, and add to CJ's great examples.

Too, also and either must have more than one thing.

In your 3 sentences, there is only one thing - "cake".

CJ gives the second thing - "pie".
There are 3 combinations: 1 - you can have both cake and pie. 2 - You can only have one, but not both. 3- you get nothing.

1) You can have cake and you can have pie. (You can have both because you have a very big plate):
You can have your cake, and your pie, too.
You can have your pie, and you can also have your cake.

2) You can only have one, but you cannot have both (they both won't fit on your small plate)

a) You can have your pie, but you can't have your cake too.
(the pie is on your plate, and you can't put cake with the pie - you can not add the cake.)

b)You can't have your cake, but you can have your pie.
(the plate is empty - no cake, so you can put the pie on it. You cannot say "too" or "also" because there is nothing to add to. Remember, too and also need more than one thing together. )

c) You can either have your cake or have your pie. (either... or is a common pair of conjunctions.)

3) You can't have anything - no cake and no pie.
You can't have your cake and you can't have your pie, either.
Woow!!
How clear and nice!!
Gotcha!!

Thanks!!

But, ...can I ask one more?
Are the following sentences correct?

You can have your pie, and you can have your cake(,) either.
You can't have your pie, and you can't have your cake(,) too.

If they aren't, why is it?

I think either is used in positive statements as follows for example.
Either is OK.
I know either boy.

So I think the first sentence is correct and means "You can have both."

I think too is used in negaive statements as your example below.
You can't have your pie, but you can't have your cake(,) too.

So I think the second sentence is correct and means:
"You can't have either. You can't have anything - no cake and no pie."
"You can't have your pie, but don't think you can have your cake. I won't give you your cake. If you think you can have your cake, you've got another thing coming."

Am I mistaken?
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If I am not mistaken, regardless of the "too" and "either" logic, the correct idiomatic expression is "you can't have the cake and eat it too", instead of "your" cake?.
GoodmanIf I am not mistaken, regardless of the "too" and "either" logic, the correct idiomatic expression is "you can't have the cake and eat it too", instead of "your" cake?.

Goodman:
I have always heard "your cake". It emphasizes the selfishness and greediness which is inherent in the adage.
You can have your pie, and you can have your cake(,) either. >> No, because "either" means the choice between 2, not the addition of 2.

You can't have your pie, and you can't have your cake(,) too.>> Yes. "too" and "also" can be used for actions as well as things.
This is saying that you can't have anything!

I think either is used in positive statements as follows for example.
Either is OK.>> Yes. This means that I give you the choice of cake or pie, and you want one of them, but you don't care which one.

I know either boy.>>
Suppose there are 2 boys (Joe and John).
I know both boys. >> I know Joe and I know John.
I know neither boy. >> I don't know Joe and I don't know John.

I know either boy. >> It does not make logical sense, but I can say:

I might know either boy. >> I might know Joe and I might know John, but I don't know both of them. I am not sure which one of them I do know.
northwindYou can't have your pie, but you can't have your cake(,) too.
Here you have to say "and", not "but", because both sides are negative. "but" is used when one is postivie and the other one is negative.

The saying: You can't have your cake and eat it too.
"have" here means to keep.
This means that if you eat your cake, you will not have it anymore.
If you keep your cake, it is obvious that it has not been eaten.
You have to make a choice between 1) eating the cake and 2) keeping the cake. You cannot do both!
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