xor === (p and not q) or (q and not p) 

expand the 'not's
    === (p and (q nor q)) or (q and (p nor p))

expand the 'and's
    === ((p nor p) nor ((q nor q) nor (q nor q))) 
     or ((q nor q) nor ((p nor p) nor (p nor p)))

expand the 'or's
    === (((p nor p) nor ((q nor q) nor (q nor q))) 
     nor ((q nor q) nor ((p nor p) nor (p nor p))))
    nor (((q nor q) nor ((p nor p) nor (p nor p))) 
     nor ((p nor p) nor ((q nor q) nor (q nor q))))