By equivalent I mean, each hypothesis can be deducted from the other.

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    Yes: "all swans are white” is "if it is a swan, then it is white". – Mauro ALLEGRANZA Jun 8 '16 at 19:55


All swans are white:

∀x(Sx → Wx)

If it is not white then it is not a swan:

∀x(~Wx → ~Sx)

Generally, p → q is equivalent to ~q → ~p. The latter is the contrapositive of the former. Similarly, the above two formulations are equivalent.

| improve this answer | |
  • Why "generally"? – kaspersky Jun 9 '16 at 6:32
  • @gg.kaspersky p → q is a more general form, and Sx → Wx is a particular case, that's all. – Eliran Jun 9 '16 at 8:31

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