I.   Here are alternate ways to express the exclusive-or:

           A.   (P v Q) & ~(P & Q) ; probably the most intuitive way

           B.   (P v Q) & (~P v ~Q)

           C.   ~P <-> Q ; the simplest way

      II.   Truth tables

           A.   [(P -> Q) & P] -> Q

           P   Q   (P -> Q)   [(P -> Q) & P]   [(P -> Q) & P] -> Q
           -------------------------------------------------------
           T   T      T                 T                     T
           T   F      F                 F                     T
           F   T      T                 F                     T
           F   F      T                 F                     T

           B.   (P <-> Q) <-> [(P & Q) v ~(P v Q)]

    P   Q   (P <-> Q)   (P & Q)   (P v Q)   ~(P v Q)   [(P & Q) v ~(P v Q)]
    -----------------------------------------------------------------------
    T   T       T          T         T          F               T
    T   F       F          F         T          F               F
    F   T       F          F         T          F               F
    F   F       T          F         F          T               T

    (P <-> Q) <-> [(P & Q) v ~(P v Q)]
    ----------------------------------
               T
               T
               T
               T

           C.   [(P -> Q) -> R] v (R <-> P)

    P   Q   R   (P -> Q)   [(P -> Q) -> R)]   (R <-> P)
    ---------------------------------------------------
    T   T   T      T                 T            T
    T   T   F      T                 F            F
    T   F   T      F                 T            T
    T   F   F      F                 T            F
    F   T   T      T                 T            F
    F   T   F      T                 F            T
    F   F   T      T                 T            F
    F   F   F      T                 F            T

    [(P -> Q) -> R] v (R <-> P)
    ---------------------------
                    T
                    F
                    T
                    T
                    T
                    T
                    T
                    T