UNIT 3 - Textbook

What is the definition of a truth-functional operator?

An operator is truth functional if and only if the truth value of the compound that it forms is completely determined by the truth values of the component parts.

What is a key property of truth-functional operators?

The truth value of the compound formed by truth-functional operators can be determined solely by the truth values of their components.

What is the rule for conjunction ('and') in truth tables?

A conjunction is true only if both conjuncts are true.

How do you determine the truth value of a disjunction ('or')?

A disjunction is false only if both disjuncts are false.

What does a biconditional operator assert?

A biconditional states that one thing happens if and only if another takes place.

When is a conditional ('if-then') considered false?

A conditional is false only when the antecedent is true and the consequent is false.

What is the truth value of negation?

Negation reverses the truth value of the formula it affects.

What differentiates truth-functional operators from non-truth-functional operators?

Truth-functional operators allow us to determine the truth value of the compound solely from the truth values of the components, while non-truth-functional operators do not.

Give an example of a non-truth-functional operator.

Examples include 'John believes that ', 'it is possible that ', or 'because __'.

How can we demonstrate that an operator is not truth functional?

To show that an operator is not truth functional, we can provide examples where the same truth values for two different sets of components lead to different truth values for the compound.

What is a shortcut when computing truth values for disjunctions?

If one disjunct is true, the entire disjunction is true.

How does one determine the validity of an argument in truth-functional logic?

By checking if an argument has any instances with true premises and a false conclusion.

What is meant by a two-valued logic?

In a two-valued logic, sentences must have a truth value that is either true or false.

How is the truth table for conjunction represented?

p q (p • q)    T T T    T F F    F T F    F F F

What does it mean for a logic to be truth functional?

A system of logic is truth functional if and only if each operator of that system is truth functional.

What are the primary properties of a truth-functional operator?

Identical truth-value input yields identical truth-value output.

What is the truth table for a biconditional?

p q (p ⇔ q)    T T T    T F F    F T F    F F T.

What is an example of how non-truth-functional operators can yield different outputs?

'It rained because the Yankees won' could be true, while 'Lincoln was president because Toyotas are made in Japan' is false, demonstrating variable output despite identical truth values.

What advantage does truth-functional logic provide in assessing arguments?

It allows for a complete and systematic determination of the truth values needed to assess argument validity.