Use your knowledge of natural deduction in predicate logic, and your knowledge of the quantifier negation rule (QN), to determine which of the following statements are true. Check all that apply.
True or False?The statement "Somebody is happy" is equivalent in meaning to the statement "It is not the case that everybody is not happy."
True or False?The quantifier negation rule can be applied to parts of lines, but not to whole lines.
True or False?The 18 propositional rules of inference, along with universal instantiation (UI), universal generalization (UG), existential generalization (EG), and existential instantiation (EI), are sufficient for completing any proof in predicate logic.
True or False?The quantifier negation rule can be applied to parts of lines.
True or False?The quantifier negation rule can be applied to whole lines, but not parts of lines.
True or False?One version of the quantifier negation rule says: (∃x)ℱx :: ~(∃x)~ℱx.
True or False?The quantifier negation rule allows you to change a universal quantifier only if that universal quantifier is preceded by a tilde.
True or False?You cannot instantiate a statement if it has a negation sign preceding the binding quantifier.
True or False?One version of the quantifier negation rule says: (x)ℱx :: ~(∃x)~ℱx.
True or False?One version of the quantifier negation rule says: ~(∃x)ℱx :: (x)~ℱx.