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)))) #### === (((p nor p) nor q) nor ((q nor q) nor p)) nor (((q nor q) nor p) nor ((p nor p) nor q))