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Propositions
- A declarative statement that can either be true or false
- “Earth is flat” → T
- “Ten is less than seven” → F
Boolean Algebra
Conditional Statements
- Negation () → not
- Conjunction () → and
- Disjunction () → or
- Exclusive Or () → xor
Variations
- Implication () → if then
- → vacuous truth
- Converse (q p)
- If you failed the course, then you did poorly on an exam
- Inverse ()
- You did not do poorly on an exam, you will not fail the course
- Contrapositive ()
- If you didn’t fail, you didn’t do poorly on a test
- Biconditional () → “if and only if”
Vacuous Truth
- If is false, is always true.
Predicates + Quantifiers
- Predicate → a function that returns a boolean value based on input
- Universal Quantifier → for all , must be true
- Existential Quantifier → there exists and where is true
Terms
- Tautology → a statement that is always true
- Contradiction → a statement that is always false
Logical Properties
- Commutative →
- Associative →
- Distributive →
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