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In: Advanced Math

Let XOR be the eXclusive OR connective Prove that the associative law applies to XOR I.e.,...

Let XOR be the eXclusive OR connective 
   Prove that the associative law applies to XOR  I.e., prove that
    (P_1 XOR (P_2 XOR P_3)) LEQV ((P_1 XOR P_2) XOR P_3).
   - Work out a simple rule to determine exactly when
      (P_1 XOR P_2 XOR ... XOR P_n)
     is satisfied.
     Prove your rule by induction on n.
 * Prove that the associative law applies to <->.  I.e., prove that
    (P_1 <-> (P_2 <-> P_3)) LEQV ((P_1 <-> P_2) <-> P_3).
   - Work out a simple rule to determine exactly when
      (P_1 <-> P_2 <-> ... <-> P_n)
     is satisfied.
     Prove your rule by induction on n.

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Colby Messinger answered 1 year ago
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