Editing Material conditional (section)

===Truth table===
From a [[classical logic|classical]] [[semantics of logic|semantic perspective]], material implication is the [[binary operator|binary]] [[truth function]]al operator which returns "true" unless its first argument is true and its second argument is false. This semantics can be shown graphically in the following [[truth table]]:
{{2-ary truth table|1|1|0|1|<math>A \to B</math>}}
One can also consider the equivalence <math>A \to B \equiv \neg (A \land \neg B) \equiv \neg A \lor B</math>. 

The conditionals <math>(A \to B)</math> where the antecedent <math>A</math> is false, are called "[[vacuous truth]]s".
Examples are ...
* ... with <math>B</math> false: ''"If [[Marie Curie]] is a sister of [[Galileo Galilei]], then Galileo Galilei is a brother of Marie Curie."''
* ... with <math>B</math> true: ''"If Marie Curie is a sister of Galileo Galilei, then Marie Curie has a sibling."''