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UNIVERSITI PENDIDKAN SULTAN IDRIS PREPARED BY : MOHAMAD AL FAIZ BIN SELAMAT
Definition : A proposition is a declarative sentence that is either TRUE or FALSE, but NOT BOT The example of declarative sentence that are not propositions: 1. Zulhelmy will not win the Thomas cup this year. x+1=3 2. Kuala Lumpur is a capital of Malaysia. 2+2=4
NotationWe use letters to denote propositional variables that representpropositions.The conventional letters used to denote numerical variable.The conventional letters used for propositional variables are p ,q , r , s ,…..The area of logic that deals with propositions is calledpropositional calculus or propositional logic.
1. Propositional Logic – NegationNegation is an other propositionsThe compound proposition is “it is not the case that p”.It called the negation of p and the denoted of ⌐p .The truth value of the negation of p is the opposite of thetruth value of p. The proposition ⌐p is also can say as “notp”.
Example 1Example : Discrete mathematics is Hasrul’s favorite subject. ( p ) Discrete mathematics is NOT Hasrul’s favorite subject.(⌐p )Truth the table for negation : p ⌐p True False False TrueThe truth table presents the relations between the truth valuesof many propositions involved in a compound proposition
2. Propositional Logic – ConjunctionConjunction is a compound proposition that hascomponents joined by the word and or its symbol.It is true only if both or all the components are true.Let p and q be propositions : The compound proposition “p and q“ . “p ˄ q”, is true when both p and q are true and false otherwise
Example 2Example : Faiz is a singer (p) and dancer (q).Truth the table for conjunction : p q p˄q T T T T F F F T F F F F
3. Propositional Logic – DisjunctionDisjunction is a proposition that presents two or morealternative terms, with the assertion that only one is true.The compound proposition “p or q“ or “p ˄ q“, is falsewhen both p and q are false and true otherwise.The compound proposition “p ˄ q“ is called disjunctionof p and q.
Example 3Example : Faiz is a singer (p) or dancer (q).Truth the table for disjunction: P Q p˄q T T T T F T F T T F F F
4. Propositional Logic – Exclusive DisjunctionExclusive Disjunction is a Logic the connective.It gives the value true to a disjunction if one or other, butnot both, of the disjunction are true.The compound proposition “p exclusive or q“, denoted“p ⊕ q“, is true when exactly one of p and q is true andis false otherwise.This compound proposition “p ⊕ q“ is called exclusivedisjunction of p and q.
Example 4Example : You can have a PS2 (p) or PSP (q).Truth the table for the exclusive disjunction: p q p⊕q T T F T F T F T T F F F