III. Let p(x) be a predicate with variable x in a universe of discourse U, and q and r be arbitrary propositions. Determine whether the following forms of argument are valid or not. (Write a short proof if the given is valid. Otherwise, provide a counterexample.) 1. (3r) p(x) → (3r) p(x) 2. (q → r) ^ q) →r

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A: The proof is given in step 2

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Q: Give an example of a valid argument of the form α ∴ ¬α

A: Negation : let A be the Statement .The statement not a a aa it is not the case that a is called the…

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A: Given- Px be the statement "x=x2". The domain consists of the integers. To find- The truth values.

Q: Show that the compound propositions (p → q) V (p → r) and (q Vr) are logically equivalent.

A: Logical equivalent statements and it is proved by using truth table

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A: Introduction: An extension of propositional logic is predicate logic. To more accurately explain the…

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Q: 8. Test the argument form shown below for validity. If you decide the argument form is not valid,…

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Q: Write a logical proof to prove that the following argument is valid. Væ(P(x) → Q(x)) Jæ (R(x) ^…

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Q: (a) Determine which of the following compound propositions are satisfiable: P)A (F → q) ^ (q → p)…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Define a model in which all of the following propositions are true. ∃x(Gx∧Hx) ∀yHy→∃z¬F z F…

A: We need to define a model in which ∃x(Gx∧Hx), ∀yHy→∃z¬Fz and Fk↔∀xGx∨Fx are true.