Say that an argument is super invalid if every model (that assigns referents/extensions to all names/predicates that appear in the argument) is a counterexample to it.(i) Without using any connectives other than negation, give an example of a super invalid argument with a single premise.(ii) Is there a proposition β such that (a) β doesn’t contain any quantifiers or the identity predicate (but β may contain any of the connectives) and (b) the argument you gave in part (i) becomes valid when β is added as a premise to it? If so, give an example of such a β. If not, explain why no such β exists.

Give an example of a model (including domain, reference and extension) that has exactly two objects in its domain and on which all of the following four propositions are true.∃y∃x(x ≠ y ∧ Syxy) → ∀z(P z → Qz) ∀x∀y∀z(Sxyz ↔ (x = z ∧ y = a))∀x(Qx → x = b) a ≠ b ∧ (Qb ↔ ∃xSxbx)

Give an example of a model that has exactly two objects in its domain and on which all of the following four propositions are true.∃y∃x(x ≠ y ∧ Syxy) → ∀z(P z → Qz) ∀x∀y∀z(Sxyz ↔ (x = z ∧ y = a))∀x(Qx → x = b) a ≠ b ∧ (Qb ↔ ∃xSxbx)

Which statement about sound arguments is true?Question 9Select one:A.Most sound arguments are valid.B.No sound arguments have premises.C.All sound arguments have two premises.D.All sound arguments are valid.E.No sound arguments are valid.

Read the following information to answer questions 7 to 9A valid argument is an argument where all the premises logically lead to the conclusion. A validargument does not have to be true, it just has to logically lead to the conclusion. A sound argument isboth valid and observably true. A cogent argument is where the premises almost certainly lead to theconclusion, but more information is needed. A fallacious argument is one where the premises cannotlead to the conclusion.Assuming that all the premises are observably true, what category do the following arguments fit into?Question 7Premise 1: Jill is a store employeePremise 2: All store employees have to wear a uniformConclusion: Jill has to wear a uniformA. ValidB. SoundC. CogentD. FallaciousE. Impossible to tellYear 8 Simulation Test – Verbal Reasoning © JAC COM Victoria Page3Question 8Premise 1: Jill makes a lot of sales: she is very good at retail.Premise 2: Jill is a Mac.Rob girl.Conclusion: Therefore, all Mac.Rob girls make a lot of sales and are very good at retail.A. ValidB. SoundC. CogentD. FallaciousE. Impossible to tellQuestion 9Premise 1: Jill is a retail workerPremise 2: No retail workers earn their living selling coffeeConclusion: Therefore, Jill does not make her living selling coffeeA. ValidB. SoundC. CogentD. FallaciousE. Impossible to tel

• Example (Gensler, 2017):IF Jane slept in, she will be late to class;Jane isn’t late to class.THEREFORE: Jane didn’t oversleep.• This is a valid inference. A valid inference is one in which the conclusion(s) follows directly from thepremises.• What does ‘follow directly’ mean? It means that it is impossible (contradictory) for the premises to be alltrue but the conclusion false.• Logic is designed to help us distinguish between ‘valid’ and ‘invalid’ arguments: i.e. ways of reasoning fromwhich reliable inferences can be drawn vs. faulty lines of argument that eventually prove nothing.• It provides a range of precise rules and techniques for making such valid inferences, and for warning usabout pitfalls along the way