I have the following doubt. I would say that This is an exclusive disjunction means "p implies not q".

Though that equivalence seems natural to me, it is not true. Could someone please give me an intuitive explanation of my error?


2 Answers 2


Follows from their definitions:

p XOR q = (p AND not q) OR (not p AND q)

p => not q = (p AND not q) OR (not p)

That is, p => not q is vacuously true when p is not true, independent of q's value.


Exclusive disjunction means p≡¬q, i.e. p⊃¬q ∧ ¬p⊃q

  • Thank you very much, this is very helpful! I guess I was missing the second part of the equivalence.
    – julian_arg
    Commented Apr 24, 2015 at 3:09

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