TF truth, falsity, and indeterminacy

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## TF truth, falsity, and indeterminacy

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**TF truth, falsity, and indeterminacy**P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff it has the value F for any truth-value assignment. P is tf-false iff ~P is tf-true P is truth-functionally indeterminate iff it has the value T for some truth-value assignments, and the value F for some other truth-value assignments. P is tf-indeterminate iff it is neither tf-true nor th-false.**TF equivalence and consistency**P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T. A set of sentences is truth-functionally inconsistent iff it is not tf-consistent.**TF entailment and validity**A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false.**TF entailment and validity**A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.**TF entailment and validity**A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid.**TF entailment and validity**A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false. An argument of SL is truth-functionally invalid iff it is not tf-valid. An argument is tf-valid iff the premises tf-entail the conclusion.**TF properties**P is truth-functionally true iff it has the value T for any truth-value assignment. P is truth-functionally false iff ~P is tf-true. P is truth-functionally indeterminate iff P is neither tf-true nor tf-false. P and Q are truth-functionally equivalent iff P and Q do not have different truth-values for any truth-value assignment. A set of sentences is truth-functionally consistent iff there is a truth-value assignment that on which all the members of the set have the value T. A set of SL sentences truth-functionally entails a sentence P iff there is no truth-value assignment on which every member of is true and P false. An argument of SL is truth-functionally valid iff there is no truth-value assignment on which all the premises are true and the conclusion false.**shortened truth tables**Show that ~B(B&~B) is not tf-true