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The sin was to defy God’s specific instruction to not eat of that tree. It’s a lack of faith that caused the fall. He told Adam very explicitly. The serpent caused doubt in Eve but if she came directly from Adam it’s unlikely she wouldn’t know the instruction. You do raise a good point though. From the text we don’t have explicit instruction to Eve not to eat of the fruit.
Funnily enough it sounds more like a man thing to do to eat of the one forbidden tree out of a general statement given by a woman. But maybe that’s just humanity I don’t know. Interesting thought.