Intro to Logic notes15

# Intro to Logic notes15 - 15 Thursday 10:05 AM More on...

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More on translation in monadic predicate logic. ׊xሺFx׈Gxሻ ׊xFx׈׊xGx All F's are G's If everything is F then it is G ׌xሺFx&Gxሻ ׌xFx&׌xGx 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 B.

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