This panel shows the
results of linking two elements (simple variables or other
truth-functional propositions) with a given connective.
The proposition is true (you see a red background)
when the elements are both true for conjunction (AND), or the same as
either true or false
(IF AND ONLY IF), or when one of the elements is true for disjunction
(OR), or as long as the antecedent is not true at the same time that
the consequent is false for implication (ONLY IF).
The
proposition is false (you see a blue background) when one of the
elements is false for conjunction (AND), or both are false for
disjunction (OR), or they are different values for equivalence (IF AND
ONLY IF), or the antecedent is true while the consequent is false in
implication (ONLY IF).