\[ \large \text{ May 1}^\text{st}, \quad \text{ May 2}^\text{nd}, \quad \text{ June 1}^\text{st} \]

One day, Eric and Frederick is trying to figure out Greg's birthday, which is one of the dates listed above.

Greg told them that his birthday is indeed one of the dates listed above. He then told Eric and Frederick the month and the day of his birthday respectively.

The following conversation took place:

Eric: I don't know Greg's birthday.

Frederick: At first I don't know when Greg's birthday is, but I know now.

Eric: Then I also know when Greg's birthday is.

When is Greg's birthday?

Assume everyone is perfectly logical and speaks the truth.

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