LOGIC AND REASONING
da Xerxes Montes
1. Deductive reasoning
1.1. General to Specific forms.
2. Inductive reasoning
2.1. Specific to General forms
3. The Conditional
3.1. “if x then x”
3.1.1. ‘if’
3.1.2. ‘Only if’
3.1.3. ‘Is sufficient for’
3.1.4. ‘Is necessary for’
3.1.5. ‘All are’
3.1.6. ‘Either not’
3.2. Equivalent forms
4. Converse
5. Inverse
6. Contrapositive
7. Tautology
8. Mathematical statement
8.1. Operations on Statements
8.1.1. Conjugation
8.1.2. Disjunction
8.1.3. Conditional
8.1.4. Biconditional
8.1.5. Negation
8.2. Relations on Statements
8.2.1. Implication
8.2.2. Equivalence
8.3. Negations on Statements
8.3.1. Add “NOT”
8.3.2. Opposite of a statement
8.4. Negation of Compound Statements
8.4.1. Using Quantifier
8.4.2. “all, some, none”
9. Truth tables
9.1. represent truth values of compound statements
9.2. find possible cases of statements
10. Valid and Invalid Arguments
10.1. Valid argument
10.1.1. modus tollens
10.1.2. modus ponens
10.1.3. syllogism
10.2. Euler Diagram
10.2.1. Prove valid/invalid arguments
10.2.2. Represent statements
10.3. Draw conclusion based on premise given
10.4. Fallacies
10.4.1. Fallacy of the converse
10.4.2. Fallacy of the inverse
10.4.3. Other kinds of Fallacies
10.4.3.1. Ad hominem
10.4.3.2. Ad populum
10.4.3.3. Appeal to authority
10.4.3.4. False Cause
10.4.3.5. Hasty Generalization