Sarah, a cash basis taxpayer, forms a corporation by transferring the following: property with an adjusted basis of $$20,000$ and fair market value of $$100,000$; accounts receivable worth $$50,000$ with a basis of zero, and accounts payable worth $$30,000.$ In return, Sarah receives all $100$ of the shares of the corporation. On the same day, Sarah gives her assistant, Jenny, $20$ shares of corporate stock as a bonus for all of Jenny$$s hard work. Which of the following is true?

$($a$)$ Sarah recognizes $$30,000$ gain; Jenny has gross income of $$24,000.$

$($b$)$ Sarah recognizes $$20,000$ gain; Jenny has gross income of $$24,000.$

$($c$)$ Sarah recognizes zero gain; Sarah$$s basis in her stock is $$16,000.$

$($d$)$ Sarah recognizes zero gain; Sarah$$s basis in her stock is $$20,000.$

$($e$)$ Sarah$$s basis in her stock is zero; Jenny$$s basis in her stock is $$24,000.$