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Unformatted text preview: ECS20 Handout 1 January 4, 2011 1. A proposition is a statement that is either true (T) or false (F), but not both. Standard notation for a proposition: p , q , r , ... 2. New propositions, called compound proposition , are formed from existing propositions using logical operations 3. Four basic compound propositions: (a) Negation of p : ¬ p = “It is not the case that p ” (b) Conjunction of p and q : p ∧ q = “ p and q ” (c) Disjunction of p and q : p ∨ q = “ p or q ” (“inclusive or”) (d) Exclusive disconjunction of p and q : p ⊕ q = “this is true either p or q but not both are ture” Truth tables display the relationships between the true values of propositions: p ¬ p T F F T p q p ∧ q T T T T F F F T F F F F p q p ∨ q T T T T F T F T T F F F p q p ⊕ q T T F T F T F T T F F F 4. The Implication p → q is the proposition “if p then q ”, p is called hypothesis , and q is called the conclusion ....
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- Winter '08
- Logic, Logical connective