Math Logic Flashcards
a statement that may be true or false
proposition
Enumerate the 5 connectives of compound propositions
- Negation
- Conjunction
- Disjunction
- Implication
- Biconditional
3 kinds of implication
- Converse
- Inverse
- Contrapositive
switching of orders ng proposition; q –> p
Converse
negation of proposition; ~q –> ~p
inverse
switching of orders and negation ng proposition; ~q –> ~p
contrapositive
3 terms under logical equivalence
- tautology
- contradiction
- contingency
proposition that is always true
tautology
proposition that is always false
contradiction
neither tautology nor contradiction
contingency
assumption; where we draw our conclusions
premises
templates to construct valid argument
rules of inference
result of assumptions
conclusion
set of premises with one conclusion
argument
8 types of inference rules
- Modus ponens
- Modus tollens
- Hypothetical syllogism
- Disjunctive syllogism
- Addition
- Simplification
- Conjunction
- Resolution
if p then q
p
therefore q
Modus ponens
if p then q
not q
therefore not p
Modus tollens
- if p then q
- if q then r
therefore if p then r
Hypothetical syllogism
- p or q
- not p
- therefore q
Disjunctive syllogism
- p
- therefore p or q
Addition
p and q
therefore q
or
therefore q
Simplification
p
q
therefore p and q
Conjunction
p or q
not p or r
therefore q or r
Resolution
10 logical equivalences
- Identity laws
- Domination laws
- Indempotent laws
- Double negation laws
- Absorbtion laws
- Negation laws
- Commutative laws
- Associative laws
- Distributive laws
- De morgan’s laws
