Joe and John intend to enter into a like$-$kind exchange of real property qualifying for tax treatment under section $1031$ of the Internal Revenue Code. Joe transfers land with a tax basis of $$100,000$ and fair market value of $$400,000,$ subject to a mortgage of $$100,000$ to John. John transfers land worth $$350,000$ subject to a mortgage of $$50,000.$

Please calculate the following just for Joe:

a$.$ what is the amount realized $($property received $+$ liability relief$)?$

b$.$ what is the Basis $($Basis in Property Given $+$ Liability Taken$)?$

c$.$ what is the Gain Realized?

d$.$ what is the Net Liability Relief $+$ Boot?

e$.$ what is the Gain Recognized: Lesser of Net Liability Relief or Gain Realized?