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LOGIC AND REASONING, MATHEMATICAL PROOFS - Coggle Diagram
LOGIC AND REASONING
Propositions
Truth Values
True denoted by T
Negation: p vs. -p
False denoted by F
Declarative & Complete
Either not Both
True
False
Compound proposition
Tautology
Logical Equivalence (if p⇔q is a Tautology)
implication and its logical equivalent
The converse and inverse of an implication
Double Negation
Equivalence Laws
Commutative
Idempotent
De Morgan's
Associative
Disributive
Always True
Contradiction
Always False
Opposite of Tautology
Contingency
Neither Tautology or Contradiction
Varying truth values
Binary Propositional Connectives
Truth tables
Truth value
Proposition
p
Proposition
q
T or F
Symbols
Conjunctions: ^
Disjunction: v
Xor: ⊕
Implication: →
Biconditional: ⇔
Conditional Propositions
p -> q
Inverse
-p -> -q
Contrapositive
-q -> -p
Converse
q -> p
Universe of Discourse
Universal set U
Quantifiers
Universal Quantification
ALL
Existential Quantification
SOME
MATH AS A LANGUAGE
MATHEMATICAL PROOFS
Rules of Inference
Addition
Simplification
Conjunction
Modus ponens
Modus tollens
Hypothetical syllogism
Disjunctive syllogism
Methods of proving
Vacuous
Direct
Indirect
Trivial
Fallacies
Affirming the conclusion
Begging the question or Circular reasoning
Denying the hypothesis
Types of Reasonings
Deductive
general to specific
Inductive
specific to general