Multiple choice questions from quizlet

Flashcards based on lecture notes to review key concepts and prepare for an exam.

Whats required to prove/disprove inconsistent

Definition leads to a contradiction, consistent if otherwise

Jointly satisfiable

Iff there is some valuation which makes them all true

Tautology

True on every valuation

Derivable

If premises entail a conclusion, then it is derivable; there is a derivation of every semantically valid argument

Prove entailment

Complete truth table or theorem

Disprove entailment

One line partial showing all true premises and a false conclusion

Mention qua quotation

Use 'john' has four letters

Prove a theorem

One proof

Disprove a theorem

All possible proofs

Prove a tautology

Complete truth table or theorem

Disprove tautology

Partial truth table

Jointly unsatisfiable

If there is no case where all the sentences are true at the same time

Prove equivalent

Two proofs

Disprove equivalent

All possible proofs

Prove validity

Complete truth table

Disprove validity

One line partial showing all true premises and a false conclusion

Prove contradiction

Complete tt

Disprove contradiction

One line partial

Contradiction

False on every valuation

Provable equivalence

When two sentences can be used to derive each other

Prove equivalence (truth table)

Complete truth table

Disprove equivalence (truth table)

One line partial

Entailment

If an argument is derivable, its premises entail its conclusion; every derivation has a valid truth table; entailment (no case in which you have all true premises and a false conclusion)

Prove satisfiable

Prove one line partial showing that both sentences are true at the same time (under the same conditions)

Disprove satisfiable

Disprove complete truth table

Entailment

a entails b if there is no case where a is true and b is false

Prove inconsistent

Prove one proof leading to a contradiction

Disprove inconsistent

Disprove all possible proofs

Equivalence (tt)

When two sentences have the same truth values for every valuation