Let A be an alphabet, m : A → {0, 1} be a truth assignment, T be an A-theory, o be an A-formula. True or false? Give a proof or counterexample. (a) TEø iff for every m such that m =T, we have m E ø. (b) m ET iff for every ø such that TE 4, we have m = ø. (c) m Eø iff for every T such that m ET, we have TE 4.
Let A be an alphabet, m : A → {0, 1} be a truth assignment, T be an A-theory, o be an A-formula. True or false? Give a proof or counterexample. (a) TEø iff for every m such that m =T, we have m E ø. (b) m ET iff for every ø such that TE 4, we have m = ø. (c) m Eø iff for every T such that m ET, we have TE 4.
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Transcribed Image Text:Let A be an alphabet, m : A → {0, 1} be a truth assignment, T be an A-theory, o be an
A-formula. True or false? Give a proof or counterexample.
(a) TEØ iff for every m such that m ET, we have m = 0.
(b) m ET iff for every o such that TEø, we have m E .
(c) m Eø iff for every T such that m =T, we have T=4.
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