Taxpayer purchased a $100$ shares of ABC stock at $$10$ per share $5$ years ago. In June of this year, he sells $50$ of those shares for $$11$ per share. He repurchases them a day later for $$10\mathrm{.}50$ per share.

Is this a wash sale?

What is his recognized gain or loss?

What is the new basis for the repurchased shares?