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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'tautology'
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Is the last statement true? by pbruin
Correction id: 6995
Filed on: 2005-08-13 10:28:06
Status: Accepted on 2005-08-13 12:33:18
Type: Erratum
Correction text:
Hi,
I'm no expert in logic, but the following statement doesn't look true to me:
(forall x)(A(x) -> B(x)) -> (exists x)(A(x) and B(x))
It is only true if there exists an x with A; for example, take A to be ``is a black cat with two heads and three tails'' and B ``is black'', then A(x) -> B(x) for all x, but there is no x with A(x) and B(x). There is also a typo in the last sentence (`abd').
Thanks,
Peter
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Comment from object owner rspuzio:
Hi,
I'm no expert in logic, but the following statement doesn't look true to me:
(forall x)(A(x) -> B(x)) -> (exists x)(A(x) and B(x))
It is only true if there exists an x with A; for example, take A to be ``is a black cat with two heads and three tails'' and B ``is black'', then A(x) -> B(x) for all x, but there is no x with A(x) and B(x). There is also a typo in the last sentence (`abd').
Thanks,
Peter
This statemennt was a misprint |
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