Philosophical Logic 2. Use a tree to test whether the following two propositions are equivalent. (Present thetree, and say whether they're equivalent or not.) If they're not equivalent, read off fromyour tree a model on which the propositions have different truth values (and indicate thepath from which you are reading it off).Vr(Ar → Gr)Ex (Ar → Gx)

Answered: 2. Use a tree to test whether the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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)

Expert Solution

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:

$for all x left parenthesis A x rightwards arrow space G x right parenthesis$
$there exists x left parenthesis A x space rightwards arrow space G x right parenthesis$