in which cases is a conditional statement of the form if a then b false
Material conditional The circle on the left bounds all members of set   A  {\displaystyle A} , and the one on the right bounds all members of set   B  {\displaystyle B} . The red area describes all members for which the material conditional is true, and the white area describes all members for which it is false. The material conditional differs significantly from a natural language's "if...then..." statement. It is only false when both the antecedent   A  {\displaystyle A}  is true and the consequent   B  {\displaystyle B}  is false.]]