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### 20 Cards in this Set

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 Quantifier of PL An expression of PL of the form (∀x) or (∃x). (∀x) = Universal quantifier. (∃x) = Existential quantifier. Sentence of PL A formula P of PL is a sentence of PL iff no occurrence of a variable in P is free. What is the contradictory of (∀x)(P⊃Q)? (∃x)(P & ~Q) What is the contradictory of (∀x)(P ⊃ ~Q)? (∃x) (P&Q) A (∀x) (P ⊃ Q) E (∀x) (P ⊃ ~Q) I (∃x) (P & Q) O (∃x) (P & ~Q) (∀y) (∀x) Lyx "Everyone likes everyone." (∃y) (∃x) Lyx "Someone likes someone." (∀x) (∃y) Lxy "Everyone likes someone." (Ey) (∀x) Lxy "Someone is liked by everyone." Quantificational Inconsistency Γ has a closed truth tree. Quantificational consistency Γ is not quantificationally inconsistent; if Γ does not have a closed truth tree. Quantificational truth The set [~P] has a closed truth tree. Quantificational Falsity The set [P] has a closed truth tree. Quantificational Indeterminacy Neither the set [P] nor the set [~P] has a closed truth tree. Quantificational Equivalence P and Q of PL/PLE are quantificationally equivalent iff the set [~(P≡Q)] has a closed truth tree. Quantificational Entailment Γ ∪ {~P} has a closed truth tree (Where Γ -a finite set- entails P -a sentence-) Quantificational validity An argument of PL/PLE with a finite number of premises is quantificationall valid iff the set consisting of the premises and the negation of the conclusion has a closed truth tree.