$(1)$ Carol owns $4,000$ shares of the stock of ABC Corporation. In $2019,$ in exchange for some of her shares, Carol receives a check for $$400,000.$ Her basis in her entire interest in ABC Corp was equal to $$1,000,000,$ and her adjusted basis of the exchanged shares is equal to $$250,000.$ ABC had $$1,200,000$ of Earnings & Profits as of the end of the $2019$ tax year. In $2018,$ Carol sustained stock market losses equal to $$175,000$ and has a LTCL carryover to $2019$ equal to $$172,000.$

$($a$)$ Assuming she has no other items of income or loss in $2019$ and does not itemized her deductions, what are the tax consequences to Carol if the redemption of her shares does not qualify for sale or exchange treatment under $302?$

$($b$)$ Assuming she has no other items of income or loss in $2019$ and does not itemized her deductions, what are the tax consequences to Carol if the redemption of her shares does qualify for sale or exchange treatment under $302?$

$(2)$ DEF Corporation has $10,000$ shares of voting common stock outstanding. Ann owns $7,000$ shares and Ben owns $3,000$ shares. Ann and Ben attended the same college, but they are not related. Which of the following transactions would constitute a redemption satisfying the requirements of $302($a$)$:

$($a$)$ DEF Corporation acquires $3,200$ shares from Ann

$($b$)$ DEF Corporation acquires $4,000$ shares from Ann

$($c$)$ DEF Corporation acquires $1,000$ shares from Ben.

$($d$)$ DEF Corporation acquires $5,100$ shares from Ann and $1,000$ shares from Ben at the same time.

$($e$)$ Assume that DEF acquired $4,200$ shares from Ann and nine $(9)$ months later redeemed $1,800$ shares from Ben.

$(3)$ XYZ Corporation redeems a portion of its stock owned by one of its shareholders, Black. The corporation redeems Black's shares by distributing to him a parcel of real property with a FMV of $$420,000$ and an adjusted basis in the hands of XYZ Corporation of $$245,000.$ What is the amount of gain, if any; XYZ Corporation will recognize that under the following circumstances?

$($a$)$ The redemption fails to satisfy any of the tests of $302($b$)$ and therefore fails to fit within the provisions of $302($a$)$ and is required to be tested under $301?$

$($b$)$ The redemption satisfies the test set forth in $302($b$)(2)$ and therefore does fit within the provisions of $302($a$).$

$(4)$ Two unrelated individuals, Aaron & Burr, own the stock of ABC Corporation. ABC redeems all of Aaron's stock in a transaction that fits within the provisions of $302($a$).$ ABC had earnings and profits equal to $$80,000.$ The corporation$$s assets have a fair market value equal to $$400,000$ and liabilities equal to $$280,000.$

$($a$)$ What is the proper amount, if any, of the reduction of ABC$$s earnings and profits if Aaron received a $$60,000$ check in exchange for her ABC stock?

$($b$)$ What is the proper amount, if any, of the reduction of ABC$$s earnings and profits if the corporation$$s assets were worth $$340,000,$ and Aaron received $$30,000$ in exchange for his X Corporation stock?