diff --git a/Logic/Boolean_functions.md b/Logic/Boolean_functions.md deleted file mode 100644 index 7e78972..0000000 --- a/Logic/Boolean_functions.md +++ /dev/null @@ -1,19 +0,0 @@ ---- -categories: - - Mathematics -tags: [logic] ---- - -# Boolean functions - -An example of a Boolean function: - -$$ -f(x,y,z) = (x \land y) \lor (\lnot(x) \land z ) -$$ - -Here is a work through where $f(1, 0, 1)$: - -// Insert diagram - -We can compute all possible outputs of the function by constructing a truth-table with each possible variable value as the diff --git a/Logic/Consistency.md b/Logic/General_concepts/Consistency.md similarity index 100% rename from Logic/Consistency.md rename to Logic/General_concepts/Consistency.md diff --git a/Logic/Indeterminacy.md b/Logic/General_concepts/Indeterminacy.md similarity index 100% rename from Logic/Indeterminacy.md rename to Logic/General_concepts/Indeterminacy.md diff --git a/Logic/Logical_equivalence.md b/Logic/General_concepts/Logical_equivalence.md similarity index 100% rename from Logic/Logical_equivalence.md rename to Logic/General_concepts/Logical_equivalence.md diff --git a/Logic/Logical_possibility_and_necessity.md b/Logic/General_concepts/Logical_possibility_and_necessity.md similarity index 100% rename from Logic/Logical_possibility_and_necessity.md rename to Logic/General_concepts/Logical_possibility_and_necessity.md diff --git a/Logic/Logical_truth_and_falsity.md b/Logic/General_concepts/Logical_truth_and_falsity.md similarity index 100% rename from Logic/Logical_truth_and_falsity.md rename to Logic/General_concepts/Logical_truth_and_falsity.md diff --git a/Logic/Object_language_and_meta-language.md b/Logic/General_concepts/Object_language_and_meta-language.md similarity index 100% rename from Logic/Object_language_and_meta-language.md rename to Logic/General_concepts/Object_language_and_meta-language.md diff --git a/Logic/Soundness.md b/Logic/General_concepts/Soundness.md similarity index 100% rename from Logic/Soundness.md rename to Logic/General_concepts/Soundness.md diff --git a/Logic/Syllogism.md b/Logic/General_concepts/Syllogism.md similarity index 100% rename from Logic/Syllogism.md rename to Logic/General_concepts/Syllogism.md diff --git a/Logic/Validity_and_entailment.md b/Logic/General_concepts/Validity_and_entailment.md similarity index 100% rename from Logic/Validity_and_entailment.md rename to Logic/General_concepts/Validity_and_entailment.md diff --git a/Logic/Biconditional_Elimination.md b/Logic/Proofs/Biconditional_Elimination.md similarity index 100% rename from Logic/Biconditional_Elimination.md rename to Logic/Proofs/Biconditional_Elimination.md diff --git a/Logic/Biconditional_Introduction.md b/Logic/Proofs/Biconditional_Introduction.md similarity index 100% rename from Logic/Biconditional_Introduction.md rename to Logic/Proofs/Biconditional_Introduction.md diff --git a/Logic/Conditional_Elimination.md b/Logic/Proofs/Conditional_Elimination.md similarity index 100% rename from Logic/Conditional_Elimination.md rename to Logic/Proofs/Conditional_Elimination.md diff --git a/Logic/Conditional_Introduction.md b/Logic/Proofs/Conditional_Introduction.md similarity index 100% rename from Logic/Conditional_Introduction.md rename to Logic/Proofs/Conditional_Introduction.md diff --git a/Logic/Conjunction_Elimination.md b/Logic/Proofs/Conjunction_Elimination.md similarity index 100% rename from Logic/Conjunction_Elimination.md rename to Logic/Proofs/Conjunction_Elimination.md diff --git a/Logic/Conjunction_Introduction.md b/Logic/Proofs/Conjunction_Introduction.md similarity index 100% rename from Logic/Conjunction_Introduction.md rename to Logic/Proofs/Conjunction_Introduction.md diff --git a/Logic/Disjunction_Elimination.md b/Logic/Proofs/Disjunction_Elimination.md similarity index 100% rename from Logic/Disjunction_Elimination.md rename to Logic/Proofs/Disjunction_Elimination.md diff --git a/Logic/Disjunction_Introduction.md b/Logic/Proofs/Disjunction_Introduction.md similarity index 100% rename from Logic/Disjunction_Introduction.md rename to Logic/Proofs/Disjunction_Introduction.md diff --git a/Logic/Formal_proofs_in_propositional_logic.md b/Logic/Proofs/Formal_proofs_in_propositional_logic.md similarity index 100% rename from Logic/Formal_proofs_in_propositional_logic.md rename to Logic/Proofs/Formal_proofs_in_propositional_logic.md diff --git a/Logic/Negation_Elimination.md b/Logic/Proofs/Negation_Elimination.md similarity index 100% rename from Logic/Negation_Elimination.md rename to Logic/Proofs/Negation_Elimination.md diff --git a/Logic/Negation_Introduction.md b/Logic/Proofs/Negation_Introduction.md similarity index 100% rename from Logic/Negation_Introduction.md rename to Logic/Proofs/Negation_Introduction.md diff --git a/Logic/Reiteration.md b/Logic/Proofs/Reiteration.md similarity index 100% rename from Logic/Reiteration.md rename to Logic/Proofs/Reiteration.md diff --git a/Logic/Strategies_for_constructing_proofs.md b/Logic/Proofs/Strategies_for_constructing_proofs.md similarity index 100% rename from Logic/Strategies_for_constructing_proofs.md rename to Logic/Proofs/Strategies_for_constructing_proofs.md diff --git a/Logic/Atomic_and_molecular_sentences.md b/Logic/Propositional_logic/Atomic_and_molecular_sentences.md similarity index 100% rename from Logic/Atomic_and_molecular_sentences.md rename to Logic/Propositional_logic/Atomic_and_molecular_sentences.md diff --git a/Logic/Propositional_logic/Boolean_functions.md b/Logic/Propositional_logic/Boolean_functions.md new file mode 100644 index 0000000..ee7d205 --- /dev/null +++ b/Logic/Propositional_logic/Boolean_functions.md @@ -0,0 +1,21 @@ +--- +categories: + - Mathematics +tags: [logic] +--- + +# Boolean functions + +An example of a Boolean function: + +$$ +f(x,y,z) = (x \land y) \lor (\lnot(x) \land z ) +$$ + +Here is a work through where $f(1, 0, 1)$: + +- The first disjunction : $ \lnot(x) \land z $ is false because $x$ is 1 and $z$ is 1 +- The second disjunction: $x \land y$ is false because $x$ is 1 and $y$ is 0 +- The overall function returns true because the main connective is disjunction and one of the disjuncts (the second) evaluates to 1. Thus the output is 1. + +We can compute all possible outputs of the function by constructing a truth-table with each possible variable as the truth conditions and the output of the function as the truth value: diff --git a/Logic/Syntax_of_sentential_logic.md b/Logic/Propositional_logic/Syntax_of_sentential_logic.md similarity index 100% rename from Logic/Syntax_of_sentential_logic.md rename to Logic/Propositional_logic/Syntax_of_sentential_logic.md diff --git a/Logic/Truth-functional_connectives.md b/Logic/Propositional_logic/Truth-functional_connectives.md similarity index 100% rename from Logic/Truth-functional_connectives.md rename to Logic/Propositional_logic/Truth-functional_connectives.md diff --git a/Logic/Truth-tables.md b/Logic/Propositional_logic/Truth-tables.md similarity index 100% rename from Logic/Truth-tables.md rename to Logic/Propositional_logic/Truth-tables.md diff --git a/Logic/Truth-trees.md b/Logic/Propositional_logic/Truth-trees.md similarity index 100% rename from Logic/Truth-trees.md rename to Logic/Propositional_logic/Truth-trees.md diff --git a/Logic/Corresponding_material_and_biconditional.md b/Logic/Theorems/Corresponding_material_and_biconditional.md similarity index 100% rename from Logic/Corresponding_material_and_biconditional.md rename to Logic/Theorems/Corresponding_material_and_biconditional.md diff --git a/Logic/DeMorgan's_Laws.md b/Logic/Theorems/DeMorgan's_Laws.md similarity index 100% rename from Logic/DeMorgan's_Laws.md rename to Logic/Theorems/DeMorgan's_Laws.md diff --git a/Logic/Law_of_Non-Contradiction.md b/Logic/Theorems/Law_of_Non-Contradiction.md similarity index 100% rename from Logic/Law_of_Non-Contradiction.md rename to Logic/Theorems/Law_of_Non-Contradiction.md diff --git a/Logic/Law_of_the_Excluded_Middle.md b/Logic/Theorems/Law_of_the_Excluded_Middle.md similarity index 100% rename from Logic/Law_of_the_Excluded_Middle.md rename to Logic/Theorems/Law_of_the_Excluded_Middle.md diff --git a/Logic/Theorems_and_empty_sets.md b/Logic/Theorems/Theorems_and_empty_sets.md similarity index 100% rename from Logic/Theorems_and_empty_sets.md rename to Logic/Theorems/Theorems_and_empty_sets.md