Question

A. Translate the argument provided in this prompt into formal logic and then use the truth-tree decision procedure (relying on Proof Tools or pencil/pen and paper) to determine whether the argument is deductively valid or invalid (entailment / non-entailment).

b. If the argument is invalid (a case of non-entailment), determine an assignment of truth values (interpretation) to the propositional letters that would show the argument to be invalid (non-entailment).

Answer 1

Follows are the solution to the given question:

Step-by-step explanation:

Please find the correct question in the attached file.

`\\ \text{ Premise 1:} \exists y Lby \\ \text{ Premise 2: }\exists x Lxb \\ \text{ Conclusion: } Lbb`

2.

Build a real tree with the premises and reject the end.

`(\exists y)Lby \ \ \ \ \ \ \ Premise 1 \\\\(\exists x)Lxb \ \ \ \ \ \ \ Premise 2 \\\\ \sim Lbb \ \ \ \ \ \ \ \ \ \ Conclusion \ \ rejection\\\\ Lba \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \exists D \\\\ Lcb \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2 \exists D\\\`

The statement is INVALID because the tree is not shut down (because a branch is open)

3.

From the given model:

`Domain={a,b,c}\\Ext(L)={ (b,a), (c,b)}`