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Assume I have $200 and I bought stock A and stock B $100 each

Stock A, I earn 10 dollars. Stock B, I lose 10 dollars.

How much do I need to pay for US government? Is it the net earning = 0, so I don't need to pay tax. OR I need to pay tax for the 10 dollars that I earn? If that is the case, how to take care the $10 that I lose?

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Assuming this occurs in the same year, your net for the year is zero. It's reported, but zeroes out to no taxable event.

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