VIEWS: 10 PAGES: 17 CATEGORY: Engineering POSTED ON: 1/15/2013 Public Domain
LOGIC INFORMATION LOGIC INFORMATION Proportional LOGIC Propositional logic is the basic sciences to study the algorithms and logic, a very important role in programming. The process of computer work can not be separated from programs which will be translated by the system logic. With proportional logic methods, we will be able to determine the truth value (true or false) of many real sentences simply by testing or observing its forms. Proposition . Is the composition of the basic logic denoted by small letters (p, q, r, ....) which has a truth value (true) and error (false) can be represented by a declarative sentence Declarative sentence is the sentence that contains truth value true or false but it is not possible have the score. Example: p: London is the capital of British-True q: 9 plus 2 is 12 - False Proposition The opposite of declarative sentences is open, ie sentences were correct value can not be determined. Example: Who's Where did he go? Whether in the year 2100 there will be a doomsday? Is today the rain? Proportional RELATIONSHIP To combine two or more propositions required so-called propositional connectives connectives are not, and, or, if-then, if-and-only-if, if- then-else. Proposition + propositional connectives = Sentences To combine the propositions with liaison is needed syntactics rule is rule necessary to combine between propositions and Propositional connectives to generate sentences SYNTACTICS RULE Each proporsisi are sentences without any propositional connectives a. If p is a negation sentences, the sentences also note p b. If p and q is the conjunction of his sentences so that p and q are also some sentences c. If p and q is the disjunction of his sentences is p or q is also a sentences d. If p and q are sentences then the implication was that if p then q also sentences e. If p and q are sentences then it is equivalent to p if and only if q is the sentences f. If p, q and r is its conditional sentences so that if p then q else r is the sentences INTERPRETATION Is giving the truth value (true or false) on each symbolic logic proposition of a sentence . Semantic Rule (Rule Semantics) is a rule that used to determine the "truth value" of a sentence from the interpretation of Proposition SEMANTIC RULE Negative Rule (Rule of NOT) Conjunction Rule (Rule of AND) P q p and q P NOT p True True True True False True False False False True False True False False False False "Negation is true if the proposition "Conjunction is true if every is false, and vice versa negation is proposition is true, if one false if the proposition is true. " proposition is false then the conjunction is false" SEMANTIC RULE Disjunction Rule (Rule of OR) P q p OR q True True True True False True False True True False False False "disjunction is true if either proposition is true, if every proposition is false then the disjunction is false NATURE OF LOGIC ALGEBRA ^ and v Idempotent law Distributive Law p p=p p p=p p(qr)= ( pq) (pr) Legal cumulative p(q r)= (pq) (pr) p p q=q p q p=q Legal Identity Associative law pFalse= p (p q) r = p (q r) pTrue = p (p q) r = p (q pTrue = True r) pFalse= False SIFAT LOGIKA ALJABAR ^ dan v Complement Law p no t p= False not(not p)= p De Morgan Law Negation of the conjunction and disjunction not (pq)= not p not q not (pq)= not p not q SEMANTIC RULE Implication Rule Equivalence Rule (Rule IF-THEN) (Rule IF –AND ONLY IF - ) P q If p then q p q If and only if True True True True True True True False False True False False False True True False True False False False True False False True "The implication is false when the "Evaluates to true if all the same antecedent true and the value proposition” consequent false" SEMANTIC RULE Conditional Rule (Rule of IF-THEN-ELSE) p q r If p then q else r True True True True True True False True True False True False "If p is true then q is true, if p is True False False False false then the applicable r” False True True True False True False False False False True True False False False False Example • If (p and (not q)) then ((not p) or r), which is when the value p = true, q = false and r = false then set the value truth of the above sentence . The value q = false, then not q = true The p-value = true and not q = true then Value (p and (not q)) = true The p-value = true, then not p = false The value r = false then ((not p) or r) = false Result : (p and (not q)) = true ((not p) or r) false so If (p and (not q)) then ((not p) or r) false Metode Truth Tabel: P q r ~p ~q p ^ (~ q) (~ p) or r If A Then B |A| |B| T T T F F F T T T T F F F F F T T F T F T T T T T F F F T T F False F T T T F F T T F T F T F F T T F F T T T F T T F F F T T F T T QUIZ Determine the truth value of logic about the first sentence the following note p = T, q = T, r = F, s = F if 1. ((if p then q) and (if q then p)) if and only if (q or not p) Use a truth table for about two : 2. (p and (if r then s)) if and only if ((if r then (not s)) and p) TO .…. BE ..... CONTINUE