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True and False Worlds for Predicate Logic formulas

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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D4Ly
Asked:
D4Ly
  • 2
1 Solution
 
ozoCommented:
Is this homework?
What do you mean by words?
What are Q, R, V and T?
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NetExpertCommented:
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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D4LyAuthor Commented:
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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D4LyAuthor Commented:
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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