Transcription of Module 1: Basic Logic Theme 1: Propositions
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Module 1: Basic Logic Theme 1: Propositions
Module 1: Basic LogicTheme 1: PropositionsEnglish sentences are either true or false or neither. Consider the following sentences:1. Warsaw is the capital of +5= How are you?The first sentence is true, the second is false, while the last one is neither true nor false. A statementthat is eithertrueorfalsebut not both is called aproposition. Propositional Logic deals with suchstatements andcompound propositionsthat combine together simple Propositions ( , combiningsentences (1) and (2) above we may say Warsaw is the capital of Poland and2+5=3 ).In order to build compound Propositions we need rules on how to combine Propositions . Wedenote Propositions by lowercase lettersp,qorr. Let us define: Theconjunctionofpandq, denoted asp^q, is the propositionpandq;and it istruewhen bothpandqare true and false otherwise. Thedisjunctionofpandq, denoted asp_q, is the propositionporq;and it isfalsewhen bothpandqare false and true otherwise. Thenegationofp, denoted either as:por p, is the propositionIt is 1:Letp= Hawks swoop andq= Gulls glide.
3. The inverse is: p!: q. In Table 5 we compare the truth values of these propositions. Table 5: The truth table for the implication, contrapositive, converse, and inverse. p q!:!: TTT T T T TFF F T T FTT T F F FFT T T T We say that two compound propositions P and Q are logically equivalent if they have the same truth values. We shall write P Q ...
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