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10 Cards in this Set
- Front
- Back
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What is a tautology?
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If a wff takes the value T for all possible assignments of truth-values to its variables, it is said to be tautologous or a tautology.
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What is a contingency?
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If for at least one assignment it takes the value T and for at least one assignment it takes the value F, it is said to be contingent or a contingency.
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What is an inconsistency?
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If a wff takes the value F for all possible assignments of truth-values, it is said to be inconsistent or an inconsistency.
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When are A and B contrary to one another?
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Two propositions A and B are traditionally called contrary if they are never both true (although they may both be false); that is, if either one is true the other is false. To say that they are never both true is to say that their conjunction is always false, which is to say that the negatino of their conjunction, -(A&B) is always true (a tautology).
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When are A and B subcontrary to one another?
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Two propositions A and B are subcontrary if they are never both false (though they may both be true); that is, if whenever one is false the other is true. To say that they are never both false is to say taht at least one of them is true, which is to say that their disjunction, A v B, is always true (a tautology). A and B are subcontrary if and only if A v B is a tautology.
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When does a proposition A imply a proposition B?
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A proposition A implies a proposition B if whenever A is true B is true (but not necessarily conversely). A implies b if and only if A -> B is tautologous. It is sometime said that A is superimplicant or superalternate to B.
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When is a proposition A implied by B?
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A proposition A is implied by a proposition B if whenever B is true A is true (but not necessarily conversely). A is implied by B if and only if B -> A is a tautology. It is often said that A is superimplicant or superalternate to B.
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When are two propositions A and B equivalent?
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Two propositions AS and B are equivalent if whenever A is true B is true and whenever B is true A is true. A is equivalent to B if and only if A <--> B is tautologous. A and B are sometimes said to be coimplicant.
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When are two propositions A and B contradictory to one another?
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Two propositions A and B are contradictory if they are never both true and never both false either; that is, if whenever one is true the other is false and whenever one is false the other is true. It is always not the case that they have the same truth value. A and B are contradictory if and only if -(A&B) is tautologous.
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When are A and B independent?
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If none of these six relationships holds between A and B, then A and B are independent.
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