A single added word that changes the meaning of a question [closed]

I understand the OP's objection to the question's phrasing.

However there are many ways a sentence can be false. Although it's counter-intuitive, saying that a sentence is false does not imply that it's false in the most obvious way or that the contrary of the most obvious way it could be false is therefore necessarily true.

In this case, it's correct to say "false" even with the confusing wording left intact, as in "False; You can't give advice at all." So though the wording is confusing, "false" is still correct even without eliding the "only".

The question is a strange one. Certainly it's ambiguous, and therefore probably needs changing. Unless the intent of the question is to create anxiety.

The problem, as usual, is that the modal auxiliary can, like all modals, has several meanings, and they interact differently with the negative trigger only. As I've pointed out before, beware of sentences containing any mix of Negatives, Modals, and Quantifiers.

One sense of can is 'be able to', a matter of personal ability, as in

• He can only reach the top shelf if he uses a ladder.

Another sense of can is 'be allowed to', a matter of social permission, as in

• He can only cross the street if his mother's watching.

The quoted sentence

You can only give advice to a customer if they ask for it.

could have either meaning of can:

On the one hand, it could refer to the actual limits of what anybody can do, in the way of giving advice to customers -- if the customer doesn't want to listen, you're wasting your time, and probably annoying them as well. If they were to ask, though, you would have a chance to succeed. This says nothing about permission, only ability.

On the other hand, it could refer to how the employer wants people to behave to customers -- if the customer doesn't ask for advice, don't bother them with it, by order of the boss. If the customer does ask, you're allowed to give it to them. This says nothing about ability, only permission.

The issue here in my mind is that the question implies something that cannot be directly contradicted with a simple answer of true or false. If you answer false (because you cannot give advice to a customer even if they ask for it) the false implies that you can give advice to a customer if they do not ask for it. Both are valid interpretations of the answer false, and false is still the only correct answer, but the question is phrased in a way that the listener will likely be led to the latter interpretation, which is wrong.