When is a conditional statement of the form “if A then B” false?

In formal logic, specifically regarding material implication, a conditional statement of the form "if A, then B" is considered false only in one specific scenario: when the antecedent (A) is true and the consequent (B) is false. In all other combinations of truth-values for A and B, the statement is considered true.12

It is important to note that this definition applies to material implication, where the truth-value of the compound statement depends solely on the truth-values of its components rather than their meanings. Other systems, such as strict implication or those used in intuitionistic logic, employ different criteria for evaluating the truth of a conditional. Furthermore, in ordinary discourse and counterfactual reasoning, the truth conditions for "if-then" statements are often more complex and may not align with the simple truth-functional approach used in formal logic.13