Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Philosophical Logic

2. Use a tree to test whether the following two propositions are equivalent. (Present the tree, and say whether they're equivalent or not.) If they're not equivalent, read off from your tree a model on which the propositions have different truth values (and indicate the path from which you are reading it off). Vr(Ar → Gr) Ex (Ar → Gx)
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Transcribed Image Text:2. Use a tree to test whether the following two propositions are equivalent. (Present the tree, and say whether they're equivalent or not.) If they're not equivalent, read off from your tree a model on which the propositions have different truth values (and indicate the path from which you are reading it off). Vr(Ar → Gr) Ex (Ar → Gx)
Expert Solution
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Step 1: Step 1:

To determine if the two propositions are equivalent, we can use a truth tree (also known as a truth table tree or semantic tree). A truth tree is a method used in formal logic to analyze the validity or equivalence of logical propositions. We will start by negating the equivalence of the two propositions and then attempt to close branches to find a counterexample. If we can't close all branches, it means the propositions are not equivalent.

Here are the two propositions:

  1. for all x left parenthesis A x rightwards arrow space G x right parenthesis
  2. there exists x left parenthesis A x space rightwards arrow space G x right parenthesis
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