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Single Idea 9531
[filed under theme 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
]
Full Idea
If A and B are expressible in propositional calculus notation, they are 'contrary' if they are never both true, which may be tested by the truth-table for ¬(A∧B), which is a tautology if they are contrary.
Gist of Idea
'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology
Source
E.J. Lemmon (Beginning Logic [1965], 2.3)
Book Ref
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.69
The
16 ideas
with the same theme
[definitions of the main concepts in propositional logic]:
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9517
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The 'scope' of a connective is the connective, the linked formulae, and the brackets
[Lemmon]
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9516
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A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔
[Lemmon]
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9518
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A 'theorem' is the conclusion of a provable sequent with zero assumptions
[Lemmon]
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9519
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A 'substitution-instance' is a wff formed by consistent replacing variables with wffs
[Lemmon]
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9529
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A wff is 'inconsistent' if all assignments to variables result in the value F
[Lemmon]
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9531
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'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology
[Lemmon]
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9534
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Two propositions are 'equivalent' if they mirror one another's truth-value
[Lemmon]
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9530
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A wff is 'contingent' if produces at least one T and at least one F
[Lemmon]
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9532
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'Subcontrary' propositions are never both false, so that A∨B is a tautology
[Lemmon]
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9533
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A 'implies' B if B is true whenever A is true (so that A→B is tautologous)
[Lemmon]
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9528
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A wff is a 'tautology' if all assignments to variables result in the value T
[Lemmon]
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9540
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A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0
[Hughes/Cresswell]
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13422
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'Conjunctive Normal Form' is ensuring that no disjunction has a conjunction within its scope
[Bostock]
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13421
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'Disjunctive Normal Form' is ensuring that no conjunction has a disjunction within its scope
[Bostock]
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13689
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'Theorems' are formulas provable from no premises at all
[Sider]
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13520
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A 'tautology' must include connectives
[Wolf,RS]
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