Could you post the definition of when a formula is true in an interpretation?
hello guys. in a few days i have an exam. i have two problems to solve, but i couldn't do it. so please help me
1) show that "a" is false in a given interpretation if and only if "-a" (negation of a) is true in the same interpretation. and "a" is true if and only if "-a" false.
2) show that none of the formula of First order can't be false and true at the same time.
please guys help me. and if u can please keep it as simple and as "short" as it can be.
Formula "a" is true in a given interpretation if and only if it is implemented or it happens(didn't find the right word ) in any sequence of ∑. if ∑ is set of every countably sequence, Whose elements are from D. D is area of that interpretation. didn't understood it clearly but hope this is what u asked for.
This may be the final part of the definition that relies on the definition of "happens" (or whatever it is). The latter concept is most likely the heart of the matter and is defined by recursion on formulas. The part about countable sequences of elements of the domain D has to do with free variables and quantifiers, and it is needed for first-order logic. However, what is important to understand is why 1) and 2) hold for propositional logic, where the truth value is defined by recursion on formulas.
So, several questions.
(a) What source are you using? Is it not "Introduction to Mathematical Logic" by E. Mendelson by chance?
(b) What language are you using? What word did you translate as "happens"?
(c) Do you know the definition of truth of a propositional formula? Do you understand it?
(d) Can you show 1) and 2) for propositional formulas?
(e) What don't you understand about the definition of the truth of first-order formulas?