Logical Connectives
What connective reverses the truth value of a sentence?
Negation (¬)
In truth tables, what letters are used to represent the two possible truth values?
T and F
What is the name of the logical system where all connectives are truth-functional?
Truth-Functional Logic (TFL)
What is a sentence that is true on some valuations and false on others called?
A contingent sentence
What does it mean for an argument to be valid?
It is impossible for the premises to be true while the conclusion is false.
Which connective is true only when both component sentences are true?
Conjunction (∧)
What is the term for an assignment of truth values to atomic sentences?
A valuation
What does it mean for a connective to be truth-functional?
The truth value of the whole sentence is determined entirely by the truth values of its parts.
What is a sentence that is false on every valuation called?
A contradiction
When do premises entail a conclusion?
When there is no valuation where the premises are true and the conclusion is false.
Which connective represents inclusive “or,” meaning the sentence is true if either or both parts are true?
Disjunction (∨)
How many rows are required in a complete truth table with four atomic sentences?
16
What feature of meaning does TFL ignore when symbolizing English sentences?
Non-truth-functional aspects such as sarcasm, emphasis, or poetic meaning.
What is a sentence that is true on every valuation called?
A tautology
What relationship exists between entailment and validity?
If premises entail a conclusion, then the argument with those premises and that conclusion is valid.
Under what condition is a conditional sentence A→B false?
When A is true and B is false.
What formula determines the number of rows in a complete truth table with n distinct atomic sentences?
2^n
Why is the TFL conditional considered a poor translation of English “if…then”?
Because it ignores causality and other nuances of ordinary language conditionals.
When are two sentences logically equivalent?
When they have the same truth value on every valuation.
What symbol represents entailment in logic?
The double-turnstile (⊨)
What connective is true exactly when both sentences have the same truth value?
Biconditional (↔)
What does each row of a complete truth table represent?
A possible valuation
Why is “It is necessarily the case that…” not a truth-functional connective?
Because the truth value of the resulting sentence is not determined solely by the truth value of the original sentence.
What does it mean for sentences to be jointly logically consistent?
There is at least one valuation where all of them are true.
What does “⊨ C” (nothing to the left of the double-turnstile) indicate?
C is a tautology.