Logic 202 Fall '24

Brandon Kidd's Intro to Logic Course at NCSU

a valid argument instance can have all true premises and a false conclusion

false

an argument form is valid id and only if it does not have any substitution instance that has all true premises and a false conclusion

true

a sound argument can have a false conclusion

false

every statement is either a tautology, contingency, or contradiction

true

the operators of sentential logic are always truth functional

true

two statement forms can logically imply each other without being consistent

true. consistency is when two statements are true at the same time. logical implication means that if one statement is true, the other must also be true. F-F

sentential logic can have a decision procedure built for it to determine properties of sentences or sets of sentences within the language

true

English operators have their meanings specified by truth-tables

false

every substitution instance can fit into infinitely many different forms

false. every form can have infinitely many instances

we could have built our logic with more or fewer operators, sentential logics do not need to have exactly 5

true

cogent arguments guarantee their conclusions

false

every contingent statement form is consistent with at least one other statement form and inconsistent with at least one other statement form

true

every proof system has 8 inference rules

false

assumptions may be discharged in any order

false

assumptions may be made in any order

true

the premises in a proof can be used in any subproof in that proof

true

the last line included in the scope of a subproof is also the line at which that subproof is discharged

false

reaching a proof’s desired conclusion inside a subproof still constitutes a correct proof

false

in sentential logic, every statement form that is a theorem, is also a tautology

true

if within a system one is able to construct a syntactic proof for every semantically valid argument, than that system is complete

true

sentential logic is consistent and complete

true

arithmetic is consistent and complete

false

all proofs are also derivations

true

inference rules cab be used when part of a cited line matches the rule’s form

false

exchange rules can be used when the entire line cited matches the rule’s form

true

all proofs have at least one premise

false

propositional functions have truth values

false

standard predicate logic is a two-valued logic

true. standard predicate logic is either true or false.

when starting with a simple sentence, you can ad either an individual constant or a quantifier to form a well-formed formula (complete sentence) in predicate logic

false

predicate logic has one most fundamental, elementary unit, while sentential logic has two

false. sentential logic has only one most fundamental unit, while predicate logic has two

lower case letters x, y, z stand for individual constants in predicate logic

false

the role of quantifiers is to tell us how many things a proposition is true of

true

every variable that is not bound is free

true

universally quantified statements are true only when the proposition is true of everything it quantifies over and there is at least one such thing

false

negated universals logically imply that something exists

true

the scope of a quantifier is defined as the first complete formula following the quantifier

true

All of the quantifier negation rules can be understood, informally, to consist in just sliding a negation through the quantifier and changing the quantifier.

true

Compound (multiple) subjects in an existentially quantified proposition are typically treated with a disjunction.

true

A propositional function that has been filled in with an individual constant instead of having a quantifier attached contains an unbound variable

false

Venn diagrams can be used to diagram sets in propositional logic

true

Categorical quantifier negation equivalences can be derived formally

true