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Ass 2 Question 8.2

Posted by dve83 
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Ass 2 Question 8.2
October 31, 2011 11:26AM
THey ask ask to prtove that LS |- RS is not valid, Ie LS does not lead to RS, ie. there is no proof for this


LS says that There exists x such that [not R(x)] OR [not Q(x)]. Meaning is not in the one OR its not in the other... (perhaps i got this wrong, but using de morgan I get, ~(R(x) ^ Q(x)) Meanings its never in both, just in one at a time and now im thinking perhaps its not in either one at all. meaning can be T&F, F&T or F&F

where as the RS says for all x we have either R(x) or Q(x),

this means that we can never have F&F. One of the two has got to be True.

THus I choose my model as such
A (of m) = 1 2 3 4 5 6
R (of m) = 1 3
Q (of m) = 2 4

In this model we have 1 and 3 only in R and 2 and 4 only in Q. 4 and 5 are nowehere. Thus LS satisfied.
the RH says all in A have got to be in R or in Q, which it is not, thus thie RH evaluates to False.

Is my reasoning correct?

Danie van Eeden
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