Truth Tables

Using a truth-table how can you tell if a sentence is a Tautology?

the column of the main operator is ALL true

Using a truth-table how can you tell if a sentence is a Contradiction?

the column of the main operator is ALL false

What happens to the truth-value of negation (¬) in a truth table?

it flips the truth value of whatever it’s attached to

What happens to the truth-value of biconditional (←→) in a truth table?

to be TRUE, BOTH things it’s attached to need to have the SAME truth-value

ex. T or T, F or F

What happens to the truth-value of disjunction (v) in a truth table?

to be TRUE, just one of the things it’s attched to have to be TRUE

• easy to make true

What happens to the truth-value of conjunction (∧) in a truth table?

to be TRUE, both things it’s attched to have to be TRUE

• hard to make true

What happens to the truth-value of conditional (→) in a truth table?

ONLY FALSE if the antecedent is TRUE and the consequent FALSE

Using a truth-table how can you tell if a sentences are Tautologically equivalent?

the colums of the sentence’s main operator have the SAME truth values

Using a truth-table how can you show sentences are jointly consistent?

show a SINGLE valuation (row) that’s ALL true (for the main operators)

Using a truth-table how can you show sentences are jointly inconsistent?

show a FULL truth-table, where not a single valuation (row) is ALL true (for the main operators)