consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is:...
consider this first- order logic formula: ∃x P(a,x)
--> ∀y P(b,y)
and its interpretation which is:
Domain D = {1,2,3}, P{(1,1), (1,2), (1,3), (2,3), (3,1)}, a=1,
b=3.
is it valid, satisfiable, or contradictory? why?
Homework Answers
This is contradictory as because there exists some x [here it is 1,2 or 3] such that P(a,x) is TRUE. As a is 1 so we look for P(1,x) to be true. Looking in the set of values in P we find out that for x=1,2 or 3 P(1,x) is TRUE.
For all y P(b,y) must be true means P(3,1),P(3,2) and P(3,3) should be true.[as domain is 1,2,3 and b is given as 3]. This is not the case as (3,2) and (3,3) is not in the set.
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consider this first- order logic formula: ∃x P(a,x)
--> ∀y P(b,y)
and its interpretation which is:...
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is:...
consider this first- order logic formula: ∃x P(a,x) --> ∀y P(b,y) and its interpretation which is: Domain D = {1,2,3}, P{(1,1), (1,2), (1,3), (2,3), (3,1)}, a=1, b=3. is it valid, satisfiable, or contradictory? why?
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