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True and False Worlds for Predicate Logic formulas

Posted on 2004-10-20
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Last Modified: 2010-04-17
NOTE: 'for all' and 'for some' will be denoted with A and E respectively. Also, 'implies' will be denoted as -->, 'OR' will be \/ and 'AND' will be /\.

a) Ax Ey Q(x,y)

b) Ex Ey (R(x) \/ V(y))

c) Ey Ax (T(x) --> R(x,y))

What are the worlds for which these predicate formulas are true and false?
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Question by:D4Ly
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4 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 12364364
Is this homework?
What do you mean by words?
What are Q, R, V and T?
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Accepted Solution

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NetExpert earned 1500 total points
ID: 12365339
a). For any value of x, there are some values of y so that Q(x,y) is true.
b). There are some values of x and y so that R(x) is true or V(y) is true.
c). There are some values of y so that for any value of x, if T(x) is true then R(x,y) is true.

It's just the same, if you understand it you will able to read it. If you can't read it, you simply do not understand.
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LVL 9

Author Comment

by:D4Ly
ID: 12365453
yes this is hw...though it doesn't matter. I figured it all out.

Thanks a lot though NetExpert...you're answers are leading to the sufficient one I need.
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LVL 9

Author Comment

by:D4Ly
ID: 12365466
worLds, not words.

 Worlds
   - Requires to provide domains for all variables and interpretations for all predicates

ie.

Ax P(x)

World_1:
Domain for x {1,2,3} and an interpretation for P:
1 | T
2 | T
3 | T

so
Ax P(x) = T {if all x in the Domain, the interpretation of P is T, or else F}

ie2.

ExP(x)
World = {T if there is an x in the Domain so that P is T, or else F}
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