Question

Prove that the following syllogism is valid by following the steps below. My teapot is purple My teapot holds water There exist purple things that hold water a) Translate the syllogism into set-theoretic notation b) Translate your set-theoretic notation into the notation of predicate logic c) Give a proof that the syllogism is valid, similar to that given in the lecture 5 videos.

Answer 1

Qo.

ANS:

Syllogism is:

My teapot is purple

My teapot holds water

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There exist purple things that hold water

A) Translate the syllogism into set-theoretic notation.

ANS:

X∈P
(X∈Q)
   ------------
(P∩Q≠∅) OR (R∩Q≠∅)??
     
   So the conclusion is: P∩Q≠∅

B) Translate your set-theoretic notation into the notation of predicate logic.
ANS:
  
   X∈P
X∈Q
------------
∃Y∈PY∈Q ??

C) Give proof that the syllogism is valid, similar to that given in the lecture 5 videos.
  
   M = P
p(Y)=Y∈Q
p(X)∧(X∈M)⊨∃Y∈Mp(Y)
M≠∅ <--> ∃X∈U X∈M
  
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THANKS!!