The true-false section is just about knowing definitions:1. If an argument has true premises and a false conclusion, then itcannot be valid. Obviously. True premises' yielding a false conclusiondefines invalidity.2. The truth-table of an invalid argument always has a row in which all of the premises are true. Yeah, it has to. All-true premises are a key part of judging invalidity.3. All uncogent inductive arguments are weak.In uncogent arguments, the evidence doesn't "induce" the conclusion.In weak arguments, the evidence is less than 50% likely to induce the conclusion. Well, 0% (not "inducing") is less than 50%, so yeah, this is true.4. The conclusion of a sound argument is necessarily true. Right. Valid arguments guarantee truth-preservation.Sound arguments are valid arguments with all-true premises.If an argument sure to preserve the truth has true premises, its conclusion will be, too.5. If the truth-table of an argument has a row in which all premises are true, and the conclusion is also true, then the argument is valid.No, this is a common trap.Some arguments just happen to have true conclusions and true premises. Logic is about the guarantee that the conclusion will follow from the premises.Example: Dogs are mammals. Children aren't adults. Therefore, Antarctica is cold. The premises don't guarantee the conclusion, since they're not relevant to it.6. All weak inductive arguments are uncogent.If you'll recall (3), you'll see that this can't be right.There are plenty of weak arguments that, nevertheless, are cogent.There are infinitely many cogency probabilities P(c) such that 0% < P(c) < 50%.7. The truth-table of two consistent propositional statements will always ave at least one row where the statements are both true.Right, this is just a part of truth-tabling notation, so just say it's true. However, the idea, generally speaking, is false.Example: Most of the sentences in The Iliad are false. They're still consistent, though.8. A sound argument can have false premises.That's literally the opposite of what the definition of soundness says. Soundness entails that all premises to an argument are true.For translations, you need to remember your key strategy:I. Find key words or phrases that translate into operators.II. As you translate them, put the affected sentences in parentheses.III. Manage pro-forms and ellipses along the way.IV. Once there are no more operators to be translated, build the translation key for the remaining sentences, and fill them in.1. Maria won't go to the game unless Tom stays at home.~(Maria will go to the game) unless Tom stays at home. \\ "Unless means "if not". ~(Maria will go to the game) if Tom does not stay at home.(Tom does not stay at home) ⊃ ~(Maria will go to the game) \\ "If" marks an antecedent. ~(Tom stays at home) ⊃ ~(Maria will go to the game) \\ No more operators. Time for the key.T := "Tom stays at home."M := "Maria will go to the game." ~T ⊃ ~M2. Chantelle will sell her house only if the market improves.(Chantelle will sell her house) ⊃ (the market improves) \\ "Only if" marks a consequent. C := "Chantelle will sell her house."M := "The market improves." C ⊃ M3. Phil is a nice guy, but he is not a reliable friend. (Phil is a nice guy) • (he is not a reliable friend) (Phil is a nice guy) • ~(he is a reliable friend)(Phil is a nice guy) • ~(Phil is a reliable friend) \\ III. "He" refersto "Phil". N := "Phil is a nice guy."R := "Phil is a reliable friend." P • ~R4. Fido is neither clumsy nor stupid. \\ "Neither... nor..." means "it's not so that... either... or..." It ' s no t s o t h a t Fido is either clumsy or stupid.~(Fido is either clumsy or stupid) ~((Fido is clumsy) ∨ (stupid))~((Fido is clumsy) ∨ (Fido is stupid)) \\ The second "Fido is" was an ellipsis. C := "Fido is clumsy."S := "Fido is stupid." ~(C ∨ S)5.Unless Carl does something about his bad breath, he will find friends only if he doesn't open his mouth.~(Carl does something about his bad breath) ⊃ (he will find friends only if he doesn't open his mouth)~(Carl does something about his bad breath) ⊃ ((he will find friends) ⊃ (he doesn't open his mouth))~(Carl does something about his bad breath) ⊃ ((he will find friends) ⊃ ~(he opens his mouth)) ~(Carl does something about his bad breath) ⊃ ((Carl will find friends) ⊃ ~(Carl opens his mouth)) \\ "He" is referring to Carl in both instances.D := "Carl does something about his bad breath." F := "Carl will findfriends."O := "Carl opens hismouth." ~C ⊃ (F ⊃ ~O)6.Neither Tony nor Trish are good at basketball, but Trish can jump. ~((Tony) ∨ (Trish are good at basketball)) but Trish can jump.~((Tony is good at basketball) ∨ (Trish is good at basketball)) but Trish can jump. \\ Ellipsis.(~((Tony is good at basketball) ∨ (Trish is good at basketball))) • (Trish can jump) T := "Tony is good at basketball."R := "Trish is good at basketball." J := "Trish can jump."(~(T ∨ R)) • J~(T ∨ R) • J \\ The extra set of parentheses are allowed, but redundant.7. Perry will come to the party if Raquel does, and Tim won't come unless Mehran does. (Raquel does) ⊃ (Perry will come to the party), and Tim won't come unless Mehran does.(Raquel comes to the party) ⊃ (Perry will come to the party), and Tim won't come unless Mehran does. \\ Ellipsis.((Raquel comes to the party) ⊃ (Perry will come to the party)) • (Tim won't come unless Mehran does)((Raquel comes to the party) ⊃ (Perry will come to the party)) • (~(Tim will come) unless Mehran does)((Raquel comes to the party) ⊃ (Perry will come to the party)) • (~(Tim will come to the party) unless Mehran comes to the party) \\ More ellipses.((Raquel comes to the party) ⊃ (Perry will come to the party)) • (~(Mehran comes to the party) ⊃ ~(Tim will come to the party))R := "Raquel comes to the party." P := "Perry will come to the party." M := "Mehran comes to the party." T := "Tim will come to the party."(R ⊃ P) • (~M ⊃ ~T)8. You will succeed in this compny if you work hard or have connections. However, if you do not have connections, then it will take time for you to get a promotion.(you work hard or have connections) ⊃ (You will succeed in this compny) However,if you do not have connections, then it will take time for you to get a promotion.((you work hard or have connections) ⊃ (You will