Well, can you walk my dog? 1) You can take her to the park.

-I'd like to, but I'm very busy today.
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What does 1) mean among the following?

2) You are allowed to take her to the park.
3) You are able to take her to the park.

#1 can mean both 2 and 3 in this context.

Among the options provided, 1) "You can take her to the park" means that the speaker has the ability or capacity to take the dog to the park.

Among the options provided, 1) "You can take her to the park" generally means that it is possible for the person being addressed to take the dog to the park. It suggests that the person has the ability or opportunity to do so, but it does not imply permission to do so.

However, it is important to note that the intended meaning can vary depending on the context or tone in which it is said. In this case, since the response is "I'd like to, but I'm very busy today," it suggests that the person is unable to fulfill the request due to personal commitments or time constraints.