Intro to Logic notes15

Intro to Logic notes15 - 15 Thursday, August 02, 2007 10:05...

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׊xሺFx׈Gxሻ ׊xFx׈׊xGx All F's are G's If everything is F then it is G Some F's are G's There exist some F's and some G's Simple quantified statements with non‐standard connectives Identify the overall structure ሺ main connectiveሻ. 1. Symbolize the overall structure of the statement. 2. Identify the component parts of the statement and any associated quantifiers. 3. Symbolize the component parts of the statement. 4. All F's are G's A. ׊xሺFx׈Gxሻ All G's are F's B. ׊xሺGx׈Fxሻ A v B ׊xሺFx׈Gxሻ v ׊xሺGx׈Fxሻ Example 1. Everyone is happy only if everyone is friendly ׊xHx A. ׊xFx B. A׈B ׊xHx ׈ ׊xFx Universal is a conjunction of the elements in the universe. Existential is the disjunction of the elements in the universe. Example 2. No one is happy unless everyone is friendly A unless B ~B׈A ~׌xHx A. ׊xFx
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Intro to Logic notes15 - 15 Thursday, August 02, 2007 10:05...

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