Exclusive disjunction in terms of conditional

Question

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?

A helpful guide is here: http://philosophy.stackexchange.com/questions/30139/how-do-i-check-if-two-logical-expressions-are-equivalent — virmaior, Jan 30 '16 at 08:27

score 1 · Answer 1 · answered Apr 24 '15 at 01:38

1

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.

answered Apr 24 '15 at 01:38

James Kingsbery

score 1 · Answer 2 · answered Apr 24 '15 at 02:24

1

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

answered Apr 24 '15 at 02:24

Atamiri

Thank you very much, this is very helpful! I guess I was missing the second part of the equivalence. – julian_arg Apr 24 '15 at 03:09

2 Answers2